I am a lower rated (1200-1300) player, and I am quite hesitant while making sacrifices. In the current game I see that black's king is unprotected and a bishop sacrifice at f5 can open up an attack against the black king. Is this the best move in the current position?
Almost certainly Bxf5 is a winning move, but it may not be what you want to play. I asked if exf6 was legal. If it is, play it. After Black recaptures play Bg6+ and your attack is just as strong without sacrificing.
In the diagram position, Blacks position is dreadful, probably lost. If you can win without taking risks, why not?
You are not sure if the sacrifice works. That is, you do not trust your analysis. Under those circumstances, should you sacrifice and risk losing? Generally speaking not, if you have a very good position and can see other ways to make progress. Generally yes if you think that your position is bad, and the sacrifice is a last shot.
But perhaps you should sacrifice anyway, just to find out how good your analysis is. Much depends then on the circumstances of the game, Friendly skittles? Last round of tournament? But if you find that it does not work, try to learn something. What did you not see? Why did you not see it? Is there something you should now remember to look for? Did you win, but only because your opponent defended badly? You should look at these things post mortem if you opponent is willing.
I think so, yes.
Black cannot ignore the sacrifice as there is the threat of Bg6#.
Moving the queen away to make space for the king won't help: 1.. Qb6 (Qc7, Qa5) 2. Bg6+ Kd8 3. Nf7+
Same for the bishop: 1.. Bxg5 2. Bg6+ Kd7 3. Qf7#
Or the pawn: 1..d6 (d5) 2. Bg6+ Kd7 3. Nf7
So he probably has to take the bishop. You take back with your queen, threatening Qf7# now.
Same options (after 1. Bxf5 exf5 2. Qxf5):
2.. Qb6 3. Qg6+ Kd8 4. Nf7+
2.. d6 (d5) 3. e6 Bxe6 4. Qg6+ Kd7 5. Qxe7+ Kc7 6. Nf7 (4.. Bf7 5. Nxf7) (4.. Kf8 5. Nxe6+)
2.. Bxg5 3. Bxg5 Qc7 4. Qg6+ Kf8 5. Rh3 and he won't be able to parry Rf3+
2.. Bxg5 3. Bxg5 Ne7 4. Qf6 Rf8 5. Qh6 Qc7 6. Rh3 is probably the way to go, but it will be very hard to defend for Black.
Additional option: 2.. Nh6 3. Qg6+ Kf8 4. Rh3 without a good answer to Rf3+ too
This looks like a lot of variations, but basically it all boils down to either the fork on f7 (if the king manages to escape to the queenside) or the manoeuvre Rh3-Rf3 (if the king stays at the wide open kingside) that he cannot properly parry because his pieces on the queenside are so out-of-play.
I ran this through Stockfish on a decent computer for about 11 hours. You can see that after move 8 White has recouped the sacrificed piece and Black is down 4 pawns. This is decisive. However, the pawn on e7 is commanding and Black gives up a little more material. Now he's down 3 pawns and the exchange. Very ugly.
[FEN "rnbqk1nr/p2pb3/2p1p3/1p2PpNp/3P3P/2PB1Q2/PP3PP1/RNB1K2R w KQkq - 0 1"] 1.Bxf5 exf5 2.Qxf5 Bxg5 3.Bxg5 Ne7 4.Qf6 Rh7 5.Nd2 d5 6.exd6 Qd7 7.dxe7 Qe6+ 8.Qxe6 Bxe6 9.Ne4 Rxe7 10.Bxe7 Kxe7 11.O-O Na6 12.Rfe1 Re8 13.Ng3 Kd7 14.Nxh5 Rf8 15.Re5 Bd5 16.g3 b4 17.Nf4 bxc3 18.bxc3 Nc7 19.Rb1 Kc8 20.a4 Rf6 21.Re7 Bf7 22.h5 Kd8 23.Re5 Nd5 24.Nxd5 Bxd5 25.Rb7 a6 26.Ra7 Bc4 27.a5 Bd3 28.g4 Rf4 29.Rg5 Bc4 30.Rg6