White to play and win.

Makes no sense. Where's the mate?
1. gxf7
Takes the pawn, threatens promotion, and takes away g8 for a future mate.
1... Kh8
Kf8 would be mate in 1 for white with Bd6#
2. Be5
Threatens mate with the white king just moving to another square.
2... Qc5
Prevents the white king from going to e7 or the rank below, as well as threatening to capture the bishop. h7 is also protecting the g6. If the king moves to e6, the queen captures the bishop, king captures the queen, the king moves closer to white's pawn and prevents it from promoting while also trying to promote his pawns.
3. Bb2
Still threatens the mate in 1. The queen can't capture it without moving it, and would still need to protect the back rank to make sure the pawn doesn't promote. Capturing the bishop would no longer protect this rank.
3... Nc7
Prevents the white king from moving to e6, and the king has no moves to move to get the checkmate.
4. Ba1
Black needs to keep all of the squares it is protecting to stay protected, this move allows white to still threaten the checkmate, and black can now only move the pawn on the a-file.
4...-8.
The bishop moves to squares it won't get captured, as well keeping on the same diagonal to keep the threat of checkmate.

All of black's pieces defend a mating square. Black now has to move one of those pieces, allowing a soon mate
There are some extremely cool lines, such as:
1.gxf7+ kh8 2.Be5 Qc5 3.Bb2 nc7 (after concluding that nc7 doesn't hold, I looked at nb6 (yes, laugh at me) which actually seems to draw if it wasn't for 4.ke6+ with mate. The line i was looking at before I noticed this was 4.ba1?? Nd7 (the actual line I was looking at, since i still hadn't seen the ke6, was 4...a4(??) 5.Bb2(??) a3(??) 6.Ba1(??) a2(??) 7.Bb2(??) Nd7! after which black is winning, since 8.Ke6+ Nf6!! 9f8Q+ (Bxf6+? Qxf6 and a1Q+) 10.Bxf6+ Qg7. Amazing what chess blindness can do to you, I was REALLY peeved when i noticed Ke6 on every white move since #4
) 4.Ba1 Nd5+5.Ke6+ (everywhere else loses, cuz Nc3 comes with check!) nc3 6.Bxc3+ and 7.f8Q#
argh, that stupid composer sure knew what he was doing