I found 1. Bxg5+ Kxf7 2. Bxd5+ Kg7 3. Rxh7#. I don't think mate in 2 is possible, so that's my final answer!
Mate in ... ?

I found 1. Bxg5+ Kxf7 2. Bxd5+ Kg7 3. Rxh7#. I don't think mate in 2 is possible, so that's my final answer!
Good idea that mates, but there is a checkmate faster than 3 moves.

Only partially correct, correct, if Black had previously moved his pawn from d7 to d5, but this may not have been the case.
Regarding a couple of puzzles recently posted on this forum, I would like to ask the following problem. It is White's turn and of course wins, but the question is how many moves are at most required to checkmate Black and which ones are they?
How many moves does White need at most to checkmate?
One. fxg6#.
Edit: Just noticed FEN has no e.p. specified, but that doesn't look possible at first sight.
Indeed, mate in 1, but you can't decide which one :-)
Yes. (Except neither is possible according to the FEN - needs to be posted as an image.)

@MARattigan Sorry for the confusion and thanks for the hint - an image instead of the FEN would have been more appropriate.
@MARattigan: It's an official composition and - as you know - compositions do not require FENs. Because the composition is not presented as a puzzle it can be analyzed by the solver with the help of the composition conventions which supplement the missing information. The common (though poor) way of handling this position is by the PRA convention which permits you to generate 2 partial (=conditional) solutions.
Regarding a couple of puzzles recently posted on this forum, I would like to ask the following problem. It's not my composition, but I find it very illustrative and hope that you could learn in some way or another from it.
It is White's turn and of course wins, but the question is how many moves are at most required to checkmate Black and which ones are they?
How many moves does White need at most to checkmate?