

Puzzle 1
g7+ Kh7
gxf8=N+! Kh8
Rg8#
Puzzle 2
Qxd8+! Rxd8 (if Bxd8, Rc8#)
Rc8+ Rxc8
Rxc8#
Puzzle 3
Bg4
Puzzle 4
Force the Black king to go in front of the pawn, then move the White king closer.
Puzzle 5
Kf4 (there are multiple solutions according to the engine, but this is the fastest one)
Puzzle 6 is just a draw. No solution. That being said, Qg1+ (It's Black to move) quickly ends the game before there can possibly be any blunders amidst a bunch of pointless moves.
Puzzle 7
I figured out Ka6 is it, but I couldn't figure out what to do from there.