Plan to proceed in this position

Question

I have a position which the engine gives as favorable for black (black to move), but I am confused on what plan should black adopt, as white has a dangerous passed pawn and black doesn't; also exchanging the queens doesn't look good as the black knight is too slow to catch the white pawn.

Answer 1

Let's check forcing moves first.

1... Qxf2 is definitely draw.

[FEN "8/8/8/2p1p3/2Pp2P1/1knP4/3q1QK2/5B2 b - - 0 1"]

1... Qxf2 2. Kxf2 e4 (2...Kc2 { transposes to main line}) {Nd1, or Na4 too slow, so e4 is the only option. Kc2 transposes to this line.} 3. Kg3! (3. g5? Kc2 {Both sides queen, but black remains with extra pawns, winning for black}) (3. dxe4? Nxe4+ {Threatening with fork, if Black exchanges minor pieces, it's a winning pawn endgame for Black} 4. Ke1 Kc3-+ {White has to give up bishop for d pawn, and White's pawn is going nowhere} (4. Kg1 Kc3-+ {White has to give up bishop for d pawn, and White's pawn is going nowhere}) (4.Kg2 Kc3-+ {White has to give up bishop for d pawn, and White's pawn is going nowhere}) {White has to give up bishop for d pawn, and White's pawn is going nowhere}){Not letting Black to get tempo while marching to queen} Kc2 4. dxe4 d3 5. Bxd3+ Kxd3 6. Kf4 Nxe4 7. Ke5=/= {Lomonosov}

So we know that Black at least has draw. But I feel Black should win in this position. Bishop is not active, but knight is doing very good, especially when it lands to e3. Also Black's king is very active, can easily eliminate White's remaining pawns if both sides queen. So, Black probably has a winning continuation.

Some ideas:

[FEN "8/8/8/2p1p3/2Pp2P1/1knP4/3q1QK2/5B2 b - - 0 1"]

1... Qc1 {This move feels best for me. It puts the queen to h6-c1 diagonal to block white pawn which I think important. Qg5 is an alternative} (1...Qg5) 2. Qg3 {Attacking e-pawn, supporting b-pawn} Nd1 {Knight is heading to e3} 3.Be2 {Activating bishop, not much alternative though} Ne3+ 4. Kf2 Kc3 { Attacking d3} 5. Qxe5 Kd2 { Threatening Qe1, taking bishop} 6. Qh2 { Defends bishop } Qe1 7. Kf3 Nxg4 {Wins a pawn} 8.Qf4 Ne3 {Bishop is hanging again} 9. Qh2 Qb1 

Resulting position looks very promising for Black. But of course, the line is not forced, so, this continuation may not be the best. Anyway, it should give an idea to decide how to proceed in starting position.

Conclusion

I believe, Black should not play 1...Qxf2, instead should look for a win. Black should centralize the knight to e3 square, put the king into c3, where it attacks d3, should try to force White to give up g-pawn by pressing on g-pawn and bishop same time, knowing that bishop is blocked by allied pawns, and pretty much stands as a target to attack in White's crampy king-side.

Testing my Findings with Monte Carlo Simulation

I run a 10 game Manto Carlo simulation where each side has 10 minutes to finish the game. In all games, black went for the line above, starting with ...Qc1, and won all games.

[Event "?"]
[Site "?"]
[Date "2015.12.28"]
[Round "1"]
[White "Stockfish 261014 64"]
[Black "Stockfish 261014 64"]
[Result "0-1"]
[FEN "8/8/8/2p1p3/2Pp2P1/1knP4/3q1QK1/5B2 b - - 0 1"]
[PlyCount "67"]
[SetUp "1"]
[TimeControl "100/600"]

1... Qc1 { +1.68/24 11s}  2. Qg3 { -1.63/25 12s}  2... Nd1 { +2.40/25 7.4s}  3.
Be2 { -2.36/25 15s}  3... Ne3+ { +2.57/24 7.4s}  4. Kf2 { -2.68/25 12s}  4...
Kc3 { +2.71/25 11s}  5. Qxe5 { -2.85/26 14s}  5... Kd2 { +3.28/27 11s}  6. Qh2
{ -3.47/27 17s}  6... Qe1+ { +3.34/26 7.4s}  7. Kf3 { -3.47/1 0.001s}  7...
Nxg4 { +3.58/27 15s}  8. Qf4+ { -3.47/25 7.2s}  8... Ne3 { +3.58/28 7.3s}  9.
Qh2 { -3.75/25 17s}  9... Qb1 { +3.87/26 40s}  10. Kf2 { -3.05/25 7.1s}  ( 10.
Bf1+ { -3.72/27 30s}  10... Kc3 { +3.72/26 5.7s}  11. Be2 { -3.40/27 6.9s} 
11... Qb6 { +3.96/26 17s}  12. Kf2 { -3.80/22 23s}  12... Qf6+ { +5.22/27 17s} 
13. Kg1 { -4.60/25 14s}  13... Qg5+ { +5.67/28 12s}  14. Kf2 { -4.97/25 33s} 
14... Nf5 { +5.88/29 5.3s}  15. Qh3 { -4.93/23 8.4s}  15... Qf4+ { +6.20/25
7.2s}  16. Qf3 { -4.55/26 9.6s}  16... Qh4+ { +10.93/36 49s}  17. Kg1 {
-4.42/26 6.2s}  17... Ne3 { +28.79/28 7.8s}  18. Qf2 { -52.13/37 17s}  18...
Qxf2+ { +52.11/36 7.1s}  19. Kxf2 { -62.24/39 13s}  19... Kd2 { +54.84/37 4.6s}
 20. Bf3 { -89.07/39 19s}  20... Kxd3 { +58.23/38 32s}  21. Bh5 { -123.53/38
9.0s}  21... Nxc4 { +62.79/41 5.9s}  22. Bd1 { -123.53/37 5.7s}  22... Kc3 {
+M73/35 8.8s}  23. Bg4 { -298.86/37 19s}  23... d3 { +M69/35 8.1s}  24. Ke1 {
-M42/36 44s}  24... d2+ { +M47/35 8.8s}  25. Kf2 { -M36/37 17s}  25... Nb2 {
+M35/36 3.9s}  26. Ke3 { -M34/37 14s}  26... d1=Q { +M31/36 7.0s}  27. Bxd1 {
-M32/36 4.4s}  27... Nxd1+ { +M29/36 3.9s}  28. Ke2 { -M26/36 9.0s}  28... Kc2
{ +M27/35 3.8s}  29. Ke1 { -M24/35 9.8s}  29... c4 { +M25/34 3.8s}  30. Ke2 {
-M22/35 4.1s}  30... c3 { +M21/34 3.8s}  31. Ke1 { -M20/33 7.8s}  31... Kb2 {
+M19/33 3.8s}  32. Kxd1 { -M18/42 5.4s}  32... c2+ { +M17/40 3.7s}  33. Ke2 {
-M16/51 3.9s}  33... c1=Q { +M15/48 3.7s}  34. Kf2 { -M14/66 5.4s}  34... Qf4+
{ +M13/71 3.7s}  35. Kg2 { -M12/120 4.0s}  35... Kc3 { +M11/120 3.0s}  36. Kh3
{ -M10/120 0.31s}  36... Kd2 { +M9/120 0.079s}  37. Kg2 { -49.17/1 0.001s} 
37... Ke2 { +M7/120 0.015s}  38. Kh3 { -M6/120 0.039s}  38... Qg5 { +M5/120
0.012s}  39. Kh2 { -M4/1 0s}  39... Kf2 { +M3/120 0.005s}  40. Kh3 { -M2/120
0.001s}  40... Qg3# { Stockfish 261014 64-Stockfish 261014 64 2015.12.28}  ) (
10. Bf1+ { -3.74/26 29s}  10... Kc3 { +3.81/25 47s}  11. Be2 { -3.25/26 6.9s} 
11... Qb7+ { +3.87/26 32s}  12. Kf2 { -3.57/27 11s}  12... Qb6 { +3.93/26 40s} 
13. Ke1 { -3.57/25 22s}  13... Qf6 { +8.13/28 7.3s}  14. Qf2 { -6.34/27 13s} 
14... Qg6 { +13.22/29 11s}  15. Qh2 { -14.05/28 14s}  15... Qg2 { +21.86/33
7.4s}  16. Qxg2 { -39.84/32 10s}  16... Nxg2+ { +52.18/37 6.6s}  17. Kf2 {
-57.87/37 13s}  17... Nf4 { +54.92/37 4.5s}  18. Bf3 { -64.66/38 40s}  18...
Nxd3+ { +61.64/38 13s}  19. Kg3 { -73.95/38 16s}  19... Nb2 { +123.52/38 6.1s} 
20. Kf4 { -123.13/37 52s}  20... d3 { +123.55/37 9.1s}  21. Bg4 { -123.19/36
13s}  21... d2 { +123.56/36 6.3s}  22. Ke3 { -74.63/34 44s}  22... d1=Q {
+298.95/34 4.3s}  23. Bxd1 { -M40/33 5.8s}  23... Nxd1+ { +M33/35 8.1s}  24.
Ke2 { -M32/36 6.5s}  24... Nb2 { +M31/35 4.2s}  25. Ke3 { -M30/35 7.3s}  25...
Kxc4 { +M27/35 4.5s}  26. Kd2 { -M26/35 8.2s}  26... Kb3 { +M25/34 4.2s}  27.
Ke2 { -M24/33 5.3s}  27... c4 { +M23/31 4.2s}  28. Ke3 { -M22/31 7.2s}  28...
c3 { +M21/32 4.2s}  29. Kf3 { -M20/30 5.2s}  29... c2 { +M17/29 4.2s}  30. Ke4
{ -M16/30 6.5s}  30... c1=Q { +M15/30 4.8s}  31. Kf5 { -M14/32 6.6s}  31... Qh6
{ +M13/33 4.7s}  32. Kg4 { -M12/42 4.8s}  32... Qg6+ { +M11/41 4.3s}  33. Kf4 {
-M10/112 4.8s}  33... Nd3+ { +M9/106 4.1s}  34. Ke3 { -M8/120 0.047s}  34...
Qf5 { +M7/120 0.10s}  35. Ke2 { -M6/120 0.013s}  35... Kc2 { +M5/120 0.014s} 
36. Ke3 { -M4/1 0s}  36... Qf4+ { +M3/120 0.003s}  37. Ke2 { -M2/1 0.001s} 
37... Qf2# { Stockfish 261014 64-Stockfish 261014 64 2015.12.28}  ) ( 10. Bf1+
{ -3.65/24 17s}  10... Kc3 { +3.73/26 12s}  11. Be2 { -3.80/25 11s}  11... Qb7+
{ +3.73/28 7.1s}  12. Kf2 { -4.55/26 18s}  12... Qg7 { +3.73/28 7.2s}  13. Qg3
{ -3.92/24 19s}  13... Qf6+ { +4.37/23 12s}  14. Kg1 { -4.20/26 23s}  14... Kd2
{ +5.05/25 37s}  15. Bf3 { -4.20/26 6.6s}  15... Kxd3 { +5.05/26 14s}  16. Qf2
{ -4.76/22 37s}  16... Qf5 { +5.11/26 6.6s}  17. Qe2+ { -4.76/22 6.1s}  17...
Kc3 { 0.00/1 0.001s}  18. Qe1+ { -5.27/22 17s}  18... Kxc4 { +5.82/23 15s}  19.
Kf2 { -6.03/21 13s}  19... Kb3 { +6.00/23 9.7s}  20. Qa1 { -6.72/23 22s}  20...
Qc2+ { +6.13/23 22s}  21. Kg3 { -6.40/25 51s}  21... c4 { +6.74/22 14s}  22.
Qa8 { -7.67/22 19s}  22... Qg6+ { +9.13/21 10s}  23. Kh3 { -8.36/23 7.0s} 
23... Qh6+ { +12.94/23 14s}  24. Kg3 { -11.10/25 24s}  24... Qg5+ { +13.89/24
9.6s}  25. Kh3 { -7.31/25 4.2s}  25... d3 { +14.70/25 19s}  26. Qa1 { -11.77/21
17s}  26... Kc2 { +33.72/23 10s}  27. Qa2+ { -17.01/20 7.4s}  27... Kc1 {
+49.10/26 19s}  28. Qf2 { -26.58/22 11s}  28... d2 { +62.82/27 5.4s}  29. Be2 {
-M38/25 17s}  29... c3 { +M33/25 7.6s}  30. Qf8 { -49.06/24 11s}  30... d1=Q {
+M31/27 9.2s}  31. Bxd1 { -M36/25 4.6s}  31... Kxd1 { +M27/29 5.2s}  32. Qf1+ {
-M24/32 7.0s}  32... Kd2 { +M23/32 10s}  33. Qf2+ { -M22/31 7.5s}  33... Kd3 {
+M21/35 4.9s}  34. Qf1+ { -M20/28 5.3s}  34... Ke4 { +M19/36 4.9s}  35. Qh1+ {
-M18/31 2.9s}  35... Qg2+ { +M17/39 4.8s}  36. Qxg2+ { -M16/44 2.8s}  36...
Nxg2 { +M15/56 4.7s}  37. Kg4 { -M14/58 3.8s}  37... c2 { +M13/71 4.7s}  38.
Kg5 { -M12/46 3.8s}  38... c1=Q+ { +M11/92 4.6s}  39. Kf6 { -M10/80 3.6s} 
39... Qc6+ { +M9/120 1.9s}  40. Kg7 { -M8/120 0.58s}  40... Kf5 { +M7/120
0.20s}  41. Kh7 { -M6/120 0.013s}  41... Qc7+ { +M5/120 0.008s}  42. Kh6 {
-M4/120 0.003s}  42... Qb7 { +M3/120 0.003s}  43. Kh5 { -M2/1 0s}  43... Qh7# {
Stockfish 261014 64-Stockfish 261014 64 2015.12.28}  ) ( 10. Bf1+ { -3.84/28
67s}  10... Kc3 { +3.69/26 18s}  11. Be2 { -3.87/24 9.6s}  11... Qb7+ {
+3.97/25 14s}  12. Kf2 { -4.03/25 9.0s}  12... Qf7+ { +4.16/27 12s}  13. Kg1 {
-4.14/25 15s}  13... Qg7+ { +4.16/27 6.4s}  14. Kh1 { -4.62/26 37s}  14... Qb7+
{ +4.16/26 18s}  15. Kg1 { -3.02/22 8.3s}  15... Qb1+ { +4.46/27 56s}  16. Kf2
{ -3.52/23 14s}  16... Kd2 { +4.46/28 5.6s}  17. Kf3 { -3.80/24 12s}  17...
Qb7+ { +5.02/27 9.0s}  18. Kf2 { -3.94/25 12s}  18... Qf7+ { +5.02/27 5.6s} 
19. Kg1 { -5.23/28 7.7s}  19... Qg6+ { +5.29/26 15s}  20. Kf2 { -5.35/29 11s} 
20... Qf5+ { +5.94/26 25s}  21. Kg1 { -5.35/31 5.4s}  21... Qg5+ { +5.94/26
5.1s}  22. Kf2 { -5.99/30 49s}  22... Nf5 { +6.08/27 5.1s}  23. Bf3 { -6.03/23
7.5s}  23... Kxd3 { +6.43/26 13s}  24. Qh3 { -5.35/23 11s}  24... Kc3 {
+10.82/26 23s}  25. Qg4 { -4.73/21 8.8s}  25... Qxg4 { +60.25/35 7.2s}  26.
Bxg4 { -54.79/32 6.8s}  26... Ne3 { +M57/34 4.6s}  27. Bf3 { -123.56/34 9.2s} 
27... Nxc4 { +298.91/34 7.5s}  28. Kg3 { -102.45/34 4.5s}  28... d3 {
+298.93/33 4.5s}  29. Kf4 { -298.98/31 6.1s}  29... d2 { +M71/34 18s}  30. Ke4
{ -122.62/33 37s}  30... Nb2 { +M43/34 9.4s}  31. Ke3 { -M36/34 10s}  31...
d1=Q { +M37/34 4.1s}  32. Bxd1 { -M32/35 3.8s}  32... Nxd1+ { +M29/35 4.0s} 
33. Ke2 { -M26/36 4.5s}  33... Kc2 { +M27/35 4.0s}  34. Ke1 { -M28/33 3.2s} 
34... Nc3 { +M25/35 4.1s}  35. Kf2 { -M26/33 3.1s}  35... Kd3 { +M23/34 3.9s} 
36. Kf3 { -M22/32 4.8s}  36... c4 { +M21/32 3.9s}  37. Kg4 { -M20/32 4.0s} 
37... Ne4 { +M19/32 5.4s}  38. Kf4 { -M18/34 4.1s}  38... c3 { +M17/34 3.7s} 
39. Kf5 { -M16/35 4.4s}  39... c2 { +M15/35 3.6s}  40. Ke6 { -M14/36 2.7s} 
40... c1=Q { +M13/36 4.3s}  41. Kd7 { -M12/39 2.7s}  41... Qf4 { +M11/42 3.7s} 
42. Ke7 { -M10/63 3.5s}  42... Qc7+ { +M9/74 3.4s}  43. Ke6 { -M8/120 0.37s} 
43... Qh7 { +M7/120 0.31s}  44. Ke5 { -M6/120 0.049s}  44... Qg6 { +M5/120
0.032s}  45. Kf4 { -M4/120 0.005s}  45... Qg5+ { +M3/120 0.005s}  46. Kf3 {
-M2/1 0.001s}  46... Qg3# { Stockfish 261014 64-Stockfish 261014 64 2015.12.28}
 ) ( 10. Bf1+ { -3.77/25 23s}  10... Kc3 { +3.96/28 8.4s}  11. Be2 { -2.77/25
7.0s}  11... Qb7+ { +4.11/27 21s}  12. Kf2 { -3.58/25 15s}  12... Qf7+ {
+4.58/27 57s}  13. Kg1 { -3.65/28 17s}  13... Qg7+ { +4.81/25 10s}  14. Kf2 {
-4.29/28 63s}  14... Qf6+ { +4.81/26 8.1s}  15. Kg1 { -5.62/27 8.2s}  15...
Qg5+ { +4.81/26 5.3s}  16. Kf2 { -7.01/28 19s}  16... Kd2 { +4.59/25 31s}  17.
Qh1 { -4.68/22 15s}  17... Qf4+ { +4.59/25 4.9s}  18. Bf3 { -5.41/23 13s} 
18... Kxd3 { +4.65/25 4.9s}  19. Qb1+ { -4.70/23 5.6s}  19... Nc2 { +5.29/23
6.8s}  20. Qb6 { -5.13/22 18s}  20... Kc3 { +10.06/23 5.0s}  21. Qa5+ {
-11.58/23 15s}  21... Kb2 { +23.63/21 9.5s}  22. Qb6+ { -16.12/25 16s}  22...
Kc1 { +49.17/29 11s}  23. Qb3 { -17.10/27 25s}  23... Qh2+ { +52.34/34 4.8s} 
24. Bg2 { -52.38/34 7.3s}  24... d3 { +52.34/34 4.8s}  25. Qxd3 { -59.72/34
9.6s}  25... Qxg2+ { +M43/38 4.8s}  26. Kxg2 { -59.72/1 0.001s}  26... Ne1+ {
+M37/38 4.8s}  27. Kf2 { -M36/39 12s}  27... Nxd3+ { +M35/37 4.8s}  28. Kg3 {
-M34/37 11s}  28... Ne5 { +M33/36 8.7s}  29. Kf4 { -M32/36 9.0s}  29... Nxc4 {
+M31/35 4.7s}  30. Ke4 { -M30/35 7.2s}  30... Nb2 { +M29/34 7.0s}  31. Ke3 {
-M24/34 9.7s}  31... c4 { +M25/34 7.3s}  32. Kf4 { -M22/33 6.4s}  32... Kd2 {
+M23/32 4.5s}  33. Kg5 { -M20/33 5.6s}  33... c3 { +M19/32 8.6s}  34. Kf4 {
-M18/31 3.8s}  34... c2 { +M17/31 4.3s}  35. Ke5 { -M16/31 6.3s}  35... Nd3+ {
+M15/30 6.5s}  36. Ke6 { -M14/34 5.8s}  36... c1=Q { +M13/33 4.1s}  37. Ke7 {
-M12/39 3.6s}  37... Qc6 { +M11/39 4.6s}  38. Kf7 { -M10/72 3.5s}  38... Ne5+ {
+M9/78 4.1s}  39. Ke7 { -M8/120 0.36s}  39... Qb6 { +M7/120 0.39s}  40. Kf8 {
-M6/120 0.034s}  40... Qd6+ { +M5/120 0.018s}  41. Kg8 { -M4/120 0.007s}  41...
Qg6+ { +M3/120 0.007s}  42. Kh8 { -M2/120 0.003s}  42... Nf7# { Stockfish
261014 64-Stockfish 261014 64 2015.12.28}  ) ( 10. Bf1+ { -3.70/24 11s}  10...
Kc3 { +3.65/29 7.6s}  11. Be2 { -3.21/24 7.2s}  11... Qb7+ { +3.93/28 20s}  12.
Kf2 { -3.54/24 20s}  12... Qf7+ { +4.26/28 26s}  13. Kg1 { -3.81/26 12s}  13...
Qg7+ { +4.26/28 6.9s}  14. Kf2 { -3.68/26 7.1s}  14... Qf6+ { +4.51/24 12s} 
15. Kg1 { -3.93/22 12s}  15... Qg5+ { +4.89/26 12s}  16. Kf2 { -4.41/23 20s} 
16... Nf5 { +5.10/26 6.8s}  17. Qh3 { -5.61/24 15s}  17... Kd2 { +6.68/24 16s} 
18. Bg4 { -6.68/25 18s}  18... Qf4+ { +6.01/23 13s}  19. Kg1 { -5.68/25 6.6s} 
19... Ne3 { +5.99/24 8.9s}  20. Bf3 { -6.95/25 12s}  20... Kxd3 { +6.86/23
9.7s}  21. Bc6 { -8.54/27 43s}  21... Kxc4 { +7.84/24 9.1s}  22. Qc8 { -8.22/24
15s}  22... Kd3 { +9.20/25 10s}  23. Qb7 { -8.96/25 12s}  23... Qg3+ { +9.26/24
9.0s}  24. Kh1 { -8.54/27 5.7s}  24... Qe1+ { +9.51/24 10s}  25. Kh2 { -8.54/1
0.001s}  25... c4 { +11.72/25 30s}  26. Bf3 { -8.05/27 5.8s}  26... Qh4+ {
+13.43/24 8.1s}  27. Kg1 { -7.84/1 0.002s}  27... c3 { +17.34/25 14s}  28. Qb1+
{ -14.91/23 11s}  28... Kd2 { +32.61/27 28s}  29. Qa2+ { -20.49/25 11s}  29...
Nc2 { +22.64/27 14s}  30. Bc6 { -49.10/27 25s}  30... Qg5+ { +48.89/28 11s} 
31. Kf2 { -52.38/29 31s}  31... Qf6+ { +49.06/30 4.9s}  32. Bf3 { -52.25/31
4.6s}  32... Qh4+ { +M47/29 41s}  33. Kg2 { -52.30/30 21s}  33... d3 {
+29.63/29 35s}  34. Bd5 { -39.71/21 6.0s}  34... Kc1 { +M57/28 3.3s}  35. Bb3 {
-52.34/27 8.8s}  35... Ne1+ { +M59/27 11s}  36. Kf1 { -M58/27 8.3s}  36... Qh1+
{ +M61/29 3.3s}  37. Kf2 { -M56/1 0.002s}  37... Qg2+ { +M27/28 18s}  38. Ke3 {
-M48/31 3.8s}  38... Qxa2 { +M25/28 2.6s}  39. Bxa2 { -M26/29 6.5s}  39... d2 {
+M25/27 2.6s}  40. Bb3 { -M24/29 5.5s}  40... c2 { +M21/27 2.5s}  41. Bxc2 {
-M20/27 6.8s}  41... Kxc2 { +M19/28 2.7s}  42. Kd4 { -M16/28 6.7s}  42... d1=Q+
{ +M17/25 2.4s}  43. Ke5 { -M14/33 7.2s}  43... Qd7 { +M13/30 2.7s}  44. Kf6 {
-M12/41 4.2s}  44... Nf3 { +M11/36 2.3s}  45. Kg6 { -M10/1 0.001s}  45... Qe6+
{ +M9/61 2.3s}  46. Kh7 { -M8/120 0.57s}  46... Ne5 { +M7/120 0.36s}  47. Kh8 {
-M6/120 0.012s}  47... Qf6+ { +M5/120 0.008s}  48. Kh7 { -M4/120 0.002s}  48...
Qg6+ { +M3/120 0.003s}  49. Kh8 { -M2/1 0s}  49... Nf7# { Stockfish 261014
64-Stockfish 261014 64 2015.12.28}  ) ( 10. Qf2 { -3.63/25 22s}  10... Qb7+ {
+13.97/28 11s}  11. Kg3 { -8.02/29 18s}  11... Qg7+ { +10.42/31 63s}  12. Kh3 {
-39.78/35 27s}  12... Qg2+ { +44.66/33 8.2s}  13. Qxg2 { -48.94/38 9.3s}  13...
Nxg2 { +52.34/37 8.5s}  14. Bf3 { -57.12/38 14s}  14... Ne1 { +58.68/40 17s} 
15. Be4 { -58.81/39 34s}  15... Nxd3 { +63.24/39 17s}  16. Kg3 { -33.37/38 57s}
 16... Ke3 { +73.47/39 19s}  17. Bf5 { -59.58/32 7.7s}  17... Ne5 { +73.33/38
50s}  18. Kh4 { -M44/36 19s}  18... d3 { +M45/33 7.7s}  19. Kg5 { -M38/36 8.9s}
 19... d2 { +M43/35 4.7s}  20. Bc2 { -M36/35 6.9s}  20... Nxc4 { +M35/36 4.7s} 
21. Kf5 { -M34/35 7.2s}  21... Kd4 { +M31/36 5.0s}  22. Kf4 { -M30/36 8.8s} 
22... Ne3 { +M29/37 7.2s}  23. Ba4 { -M28/36 5.1s}  23... d1=Q { +M27/37 4.7s} 
24. Bxd1 { -M26/36 5.0s}  24... Nxd1 { +M25/35 4.7s}  25. Kf3 { -M22/37 8.0s} 
25... Kd3 { +M23/35 5.4s}  26. Kg2 { -M20/38 7.6s}  26... c4 { +M19/36 4.7s} 
27. Kh2 { -M18/40 6.6s}  27... c3 { +M17/39 4.7s}  28. Kg3 { -M16/42 4.9s} 
28... c2 { +M15/39 4.7s}  29. Kg4 { -M14/42 7.1s}  29... Ne3+ { +M13/43 4.9s} 
30. Kg5 { -M12/55 6.6s}  30... c1=Q { +M11/55 4.8s}  31. Kg6 { -M10/84 4.7s} 
31... Qc6+ { +M9/111 4.7s}  32. Kg7 { -M8/120 0.87s}  32... Nf5+ { +M7/120
0.070s}  33. Kf7 { -M6/120 0.004s}  33... Kd4 { +M5/120 0.009s}  34. Kg8 {
-M4/120 0.005s}  34... Qf6 { +M3/120 0.004s}  35. Kh7 { -M2/1 0.001s}  35...
Qg7# { Stockfish 261014 64-Stockfish 261014 64 2015.12.28}  ) 10... Qb6 {
+3.62/23 11s}  11. Qh8 { -3.81/24 39s}  ( 11. Bf3 { -4.08/25 59s}  11... Kxd3 {
+3.94/21 8.7s}  12. Qg1 { -4.12/21 23s}  12... Qb2+ { +4.08/20 11s}  13. Kg3 {
-4.43/21 14s}  13... Nxc4 { +4.41/21 26s}  14. Bh5 { -4.24/21 29s}  14... Ne3 {
+4.63/21 12s}  15. Bg6+ { -4.65/20 14s}  15... Kc3 { +4.75/22 30s}  16. Kf3 {
-4.94/23 44s}  16... c4 { +5.45/22 7.8s}  17. Qe1+ { -4.99/21 13s}  17... Kb3 {
+6.49/23 5.6s}  18. Ke4 { -5.93/23 16s}  18... c3 { +6.97/23 5.6s}  19. Kd3 {
-7.31/22 12s}  19... Ka3 { +7.49/24 9.0s}  20. Qh1 { -8.99/22 20s}  20... Qd2+
{ +11.19/20 7.8s}  21. Ke4 { -8.99/1 0s}  21... c2 { +11.39/22 13s}  22. Qa1+ {
-13.00/18 5.3s}  22... Kb4 { +12.91/23 23s}  23. Qb2+ { -8.88/18 6.0s}  23...
Kc5 { +13.14/24 30s}  24. Qa3+ { -10.71/20 9.4s}  24... Qb4 { +14.12/25 40s} 
25. Qc1 { -11.76/22 13s}  25... Qc3 { +14.09/25 6.1s}  26. Kf3 { -17.11/23 19s}
 26... Nf5+ { +14.15/25 35s}  27. Kg4 { -19.91/23 26s}  27... Qd3 { +18.03/21
7.0s}  28. Qf4 { -19.98/19 5.5s}  28... Qd1+ { +10.94/20 5.0s}  29. Kxf5 {
-20.46/19 8.4s}  29... c1=Q { +11.15/21 3.2s}  30. Qc7+ { -16.23/20 13s}  30...
Kb4 { +18.18/18 4.9s}  31. Qb7+ { -16.35/21 18s}  31... Kc3 { +23.17/20 10s} 
32. Qc7+ { -13.56/15 2.3s}  32... Kb2 { +39.71/21 4.3s}  33. Qb6+ { -11.17/15
4.9s}  33... Ka3 { +28.70/22 9.8s}  34. Qd6+ { -21.64/18 9.3s}  34... Ka2 {
+18.53/22 8.0s}  35. Bf7+ { -20.06/20 1.4s}  35... Kb1 { +49.10/25 2.5s}  36.
Qb8+ { -49.02/21 3.4s}  36... Qb2 { +M67/25 8.9s}  37. Qf4 { -49.10/23 2.0s} 
37... Qdc2+ { +M65/24 2.3s}  38. Kg4 { -49.62/25 6.1s}  38... Qb7 { +M21/24
11s}  39. Kh4 { -M22/19 1.7s}  39... Qh7+ { +M19/25 2.1s}  40. Bh5 { -M18/24
1.1s}  40... Qhe7+ { +M17/28 2.3s}  41. Kg3 { -M16/27 1.5s}  41... Qe1+ {
+M15/31 2.0s}  42. Qf2 { -M14/31 1.0s}  42... Qg7+ { +M13/34 2.2s}  43. Bg4 {
-M12/37 0.99s}  43... Qxf2+ { +M11/43 2.1s}  44. Kxf2 { -M10/81 0.97s}  44...
Qxg4 { +M9/100 1.9s}  45. Kf1 { -M8/120 0.11s}  45... d3 { +M7/120 0.065s}  46.
Kf2 { -M6/120 0.003s}  46... d2 { +M5/120 0.005s}  47. Ke3 { -M4/120 0.005s} 
47... d1=Q { +M3/120 0.005s}  48. Kf2 { -M2/1 0s}  48... Qgg1# { Stockfish
261014 64-Stockfish 261014 64 2015.12.28}  ) ( 11. Qf4 { -3.84/25 32s}  11...
Qg6 { +4.39/25 34s}  12. Qf3 { -4.06/24 11s}  12... Qg5 { +4.56/25 24s}  13.
Qh1 { -4.46/24 24s}  13... Qf4+ { +4.89/22 5.7s}  14. Bf3 { -4.46/24 6.3s} 
14... Kxd3 { +5.50/22 11s}  15. Qb1+ { -6.26/23 38s}  15... Nc2 { +5.89/23
8.6s}  16. Qb2 { -6.49/25 22s}  16... Qh4+ { +8.75/24 5.6s}  17. Kg1 { -8.89/25
13s}  17... Qg3+ { +10.73/25 7.8s}  18. Bg2 { -10.51/27 12s}  18... Kd2 {
+10.39/26 10s}  19. Kh1 { -7.77/26 5.5s}  19... Qh4+ { +12.27/25 15s}  20. Kg1
{ -11.33/23 8.0s}  20... d3 { +12.24/26 16s}  21. Bb7 { -16.35/28 50s}  21...
Qxc4 { +17.62/26 11s}  22. Kg2 { -16.58/25 13s}  22... Qd4 { +52.18/28 7.3s} 
23. Qb1 { -31.53/27 31s}  23... Ne3+ { +M25/28 7.1s}  24. Kh1 { -M24/27 7.9s} 
24... Qh4+ { +M21/31 6.2s}  25. Kg1 { -M22/1 0.001s}  25... Qg3+ { +M19/36
5.4s}  26. Kh1 { -M18/36 5.8s}  26... Ke2 { +M17/38 5.1s}  27. Qc1 { -M16/38
4.0s}  27... Qh4+ { +M15/41 5.5s}  28. Kg1 { -M16/1 0.001s}  28... Qf2+ {
+M13/49 6.0s}  29. Kh1 { -M14/1 0s}  29... d2 { +M11/70 5.2s}  30. Ba6+ {
-M10/81 5.7s}  30... Kf3 { +M9/120 0.47s}  31. Be2+ { -M8/120 0.40s}  31...
Qxe2 { +M7/120 0.007s}  32. Qg1 { -M6/120 0.005s}  32... d1=Q { +M5/120 0.005s}
 33. Qxd1 { -M4/120 0.002s}  33... Nxd1 { +M3/120 0.003s}  34. Kg1 { -M2/1 0s} 
34... Qg2# { Stockfish 261014 64-Stockfish 261014 64 2015.12.28}  ) 11... Qd6 {
+3.95/24 20s}  12. Qh4 { -4.12/23 28s}  12... Qg6 { +4.53/24 61s}  13. Bf3 {
-4.00/23 6.4s}  13... Qxd3 { +4.83/24 54s}  14. Qh1 { -3.97/19 8.7s}  14... Nc2
{ +5.34/22 8.3s}  15. Qd1+ { -5.43/23 37s}  15... Kc3 { +5.34/1 0.001s}  16.
Qb1 { -10.45/27 29s}  16... Qxc4 { +5.94/21 7.7s}  17. Bg4 { -7.25/23 40s} 
17... d3 { +6.90/21 5.2s}  18. Kg3 { -6.25/23 5.1s}  18... Qd4 { +7.42/22 10s} 
19. Qa2 { -8.84/22 27s}  19... c4 { +8.15/24 17s}  20. Qa6 { -12.20/23 39s} 
20... d2 { +15.03/23 33s}  21. Qa8 { -12.86/24 20s}  21... Kb2 { +11.22/20
7.5s}  22. Qb7+ { -14.57/23 12s}  22... Kc1 { +13.31/22 10s}  23. Qa8 {
-14.50/24 6.0s}  23... c3 { +15.70/24 18s}  24. Bf3 { -13.50/24 5.2s}  24...
Kb2 { +52.18/18 5.8s}  25. Kh3 { -52.11/19 6.0s}  25... Nb4 { +M47/22 13s}  26.
Qa4 { -M30/21 11s}  26... c2 { +M17/23 5.3s}  27. Qxc2+ { -M16/23 4.2s}  27...
Kxc2 { +M15/33 3.9s}  28. Bg4 { -M14/33 4.9s}  28... d1=Q { +M13/33 4.3s}  29.
Bxd1+ { -M12/53 3.6s}  29... Kxd1 { +M11/57 4.0s}  30. Kg2 { -M10/113 3.5s} 
30... Qg4+ { +M9/120 3.7s}  31. Kf1 { -M8/120 0.12s}  31... Qh3+ { +M7/120
0.013s}  32. Kg1 { -M6/120 0.021s}  32... Nc2 { +M5/120 0.005s}  33. Kf2 {
-52.38/1 0s}  33... Ne3 { +M3/120 0.002s}  34. Kg1 { -M2/1 0s}  34... Qg2# {
+M1/120 0.002s, Black mates}   0-1

We can strongly(but not absolutely) believe that Black wins in this position.

Answer 2

Boiling down a lot of the previous detail:

1) As you realized, the passed pawn on g4 is the central problem for Black. At the moment it is halted by the white queen covering the nice g5 square. So the first plan is to keep that queen on the c1-h6 diagonal. That also means not allowing black to exchange it off, so the second plan has to be move the queen now to a square not covered by White's queen. That leaves Qc1, Qg5, Qh6.

2) Once Black's queen is managing the passed pawn as above, the knight is not all that slow. It can get to d1 if White doesn't play Be2, otherwise to e4 after Black forces the d3 pawn off the board by playing e4.

Answer 3

Black's best hope is for a perpetual by something like

[FEN "8/8/8/2p1p3/2Pp2P1/1knP4/3q1QK1/5B2 b - - 0 1"]


1... Qg5 2. Qf5 Qd2+ 3. Qf2

The question is can White's king escape the checks, maybe via g3 and h4, and then get in g5 when only white can win? I think the key is for black to try and keep his queen on the c1-h6 diagonal, be able to drive white's king back from h4 and prevent g5. If he can do this then he can hold the draw.