Queen first, lose (or draw) later

Question

I will soon teach my chess kiddies the laws of pawn endings. The overarching strategem is of course "Queen a pawn, Queen it first, Queen and stop calculating". Look at the easy win (Stockfish says) against even a pawn armada worth almost two queens (illegal, of course):

[FEN "8/4P3/pppppppp/pppppppp/8/4k3/8/4K3 w - - 0 1"]

But chess wouldn't be chess without exceptions. It could happen that you must assign the outcome of a queen endgame if the opponent queens too. The opponent can escape into a stalemate. The opponent might even mate you, even if the enemy pawn doesn't queen in the next move or at all!

For no peculiar reason I'd like to split the question in a) game only a draw after queening first/game even lost and b) rank of most forward enemy pawn on time of Blacks queening move, making 2*6 questions. By the (IMHO unpractical) SE rules I must now split. Fortunately, for some questions I already know the answer, and some "dominate" others, so less than 12 questions remain for you to find an economy record. (EDIT: Far less - Evargalo completely mopped up the "draw" case.) Positions should be legal! (Unless noted otherwise) Please give always the position before Black queens (and if Black makes another move, it doesn't change the result!).

1. What is the most economic pawn endgame (least number of pawns; tie: less white ones) where Black queens first and still loses, White pawn on 7th?

Split off:

• draw, rank 6 or higher, 1+1 pawn
• draw, rank 2 or higher, 1+1 pawn (rank record as well)
• win, rank 6 or higher, 1+1 pawn ("beats" the answer here by 1 row)
• draw, rank 3 or 4, 2+2 pawns
• win, lower than rank 5, 2+3 pawns

Answer 1

[FEN "k7/8/1K6/1p6/3P4/8/8/8 w - - 0 1"]

Obvious economy record. Hauke Reddmann, INSELSCHACH 1982 (no exact anticipation exists, but tons "in spirit"), White wins by 1.Kc7! ... 4...b1Q 5.d8Q+ 6.Qd4+ 7.Qa4#, i.e. mate is still two moves away after White queens! (Of course you can easily have more positions where White queens with immediate mate.)

Answer 2

4th rank, 4+1 pawns:

[Title "White plays and wins"]
[FEN "8/8/8/8/kPP5/2P5/1P5p/K7 w - - 0 0"]

1. Ka2 h1=Q 2. b3#

(Also works with 3+2 pawns, removing wPb4 or wPc4 and adding bPa5 or bPb5 respectively. All of these are drawn with bPh2 moved to c2, when Black answers 1 Ka2 with c1=N+!)

Answer 3

According to the 6-man "tablebases" White wins this 3+1 position only by forgoing promotion of either advanced pawn and instead advancing the other pawn to join its comrades on the 6th rank:

[Title "White plays and wins"]
[FEN "8/6K1/5P1P/8/6P1/8/1k4p1/8 w - - 0 0"]

1. g5! g1=Q 2. g6! 1-0

White eventually does promote at least one pawn and mates by move 32 with best play.