It's isn't legal. Try to find out how.
Illegal Position Contest!

It's isn't legal. Try to find out how.
Black’s light squared Bishop could not have moved from c8.
It's isn't legal. Try to find out how.
Black’s light squared Bishop could not have moved from c8.
That's one.

It's isn't legal. Try to find out how.
The doubled pawns, no pieces to capture have come off the board

#401: Illegal, and I see why, but I'll leave it for others to try and understand. The try with wNxBc8 (reasoning from the starting position) is interesting but leads nowhere.
#419: Legal.

It's isn't legal. Try to find out how.
The doubled pawns, no pieces to capture have come off the board
I was gonna say that

I also believe this one is Illegal
No, that looks legal. The White pawn captured a Black Knight and the Black King may have stepped out of the way for a discovered check.
This is a common trick puzzle, because it appears in a semi-famous book, but is it possible for this position to be reached with white to move?
yes of course:
1. Nc3 e5 2. Nb1
Your sequence reaches the position with black to move. The solutions are 1.Nc3 e6 2.Nb1 e5
and 1.Nf3 e6 2.Ng1 e5
In order to make it not so obvious, have the White pieces with a Bishop fianchettoed on g2 and a Bishop on c4 with all 8 pawns remaining on the board.