Castling allowed
Puzzle #1 is brilliant! #2 is wrong because the black king escapes to g2. #3 is also brilliant but the solution given is wrong.
Here is a brilliant version of #2 (probably how it was originally composed):
You don't need it. The queen/rook covers it.
After the 2nd move, yes. After the first move, no. So you need it.

You don't need it. The queen/rook covers it.
Rh6 Kg2#
The truth hurts
I really like your puzzles INwinl
Just see my correction in comment #4 is wrong because 1. Qa2 works. Here is the repair - note that the pawns on b2 and b3 are technically better than those on c2 and c3 in the original!
In the third puzzle 1 Qd4 is given. After 1. Qd4 Bb1 (preventing 0-0-0) there are five potential white checks:
a) Bxd5+ (answered by Rxd5)
b) Qxd5+ (answered by Rxd5)
c) Qe4+ (answered by Qxe4)
d) Rg1+ (answered by hg)
e) Nt3+ (answered by Kg2)
If the h7 B is replaced by a P in the initial diagram then there is nothing to prevent 2. 0-0-0# or 2 Kd2#
Btw, here's a version with the same content but saving 1 full piece which is worth $1,000,000 in compositions. Checkmate in 2 moves.
White mates in 4.