Hardest mate in 1 puzzles

Black must play g2 because it is the only way to win the game
So, is 1...Nf2# illegal, or what?

Correct.
Wrong. Black can also mate with 1...Nf2#.
That is also correct.

I mean mate in 2
There are a gazillion mate in 2 here, for example any rook move on the seventh rank.
White to move
The queen is supposed to be on e1. I've seen this puzzle. Queen b4 is the mate in 2 because it is blacks turn now and they are zugzwanged to a mate in one
I could say that the position is already mate since white appears to be in checkmate. There. Mated.
In fact, I'm not asking you to find a move that allows white to deliver mate in 1. I'm asking you if white is in checkmate already or not.
@SomethingStranger: If that was white's last move before ...c6-c5, the bishop on b8 must be promoted. Is there any reason that is possible, or impossible?
if there is en passent then it is not checkmate
Correct.