Screener, that second one is a one-mover. 1. Bf7#.
sorry
in the last puzzle rook h5
Moving the rook to h5 would take 2 moves and it is useless. Maybe you notating wrong? Perhaps you should learn how to notate before correcting others' puzzles.
Not a forced mate as Black doesn't have to promote the pawn.
21. Nh5+ or Ne8+ Kg8 22. Qg7# and 20...Kg7 was a blunder. Best move was Kh8. Then 21. Nd7+ Kg8 22. Nxf8 Kxf8
If white plays Nh5+ Black can't play Rxh5 because he's still in check by the queen. If you are double checked you have to move the king.
in the last puzzle rook h5