Legal or illegal? :) I think this one is a good one.
Looks legal to me. I don't really see what the problem is (although I had to lose a lot of tempos with the black queen at the end because I didn't spend enough time on positioning the white pieces).
You are right. :) I actually tried to setup an illegal position, but I overlooked one thing. You showed that it was legal. I made a couple changes to the diagram. Unless I overlooked something else, I believe that this diagram here is illegal.
I fail to see how that is illegal. White captured at least five of black's pieces with his pawns, but there are more than five black pieces missing, and nothing needs to be the result of a promotion. Other than that, nothing really jumps out at me other than the odd position of white's king, but it doesn't look difficult to move it there.
I think I found another flaw in my 2nd diagram. I will fix it here shortly. I will go through my steps of my thought process. The thing is that I overlooked is that there is the possibility that white has captured a black piece that black just moved (this is also the case for 2 turns ago). :) There is a lot to think about for this diagram. I'm trying to combine different concepts. You have one concept, and that is about the pawn structure. I'm factoring that into the 3rd diagram. :) I think the 3rd time will be a charm.
Answer is no, but if you took away the knight it would be, but why?
The only legal position that can lead to that position is with the black king at h2, in check, because there is nowhere the knight could have come from and the king could not have been adjacent to white's king. One tempo before that, white must have not had black in check (since it was white to move), but there is nowhere the rook could have come from, so the check must have been discovered. Without white's knight, there would be nothing to block the rook check, and the position would have been illegal.
Actually another potential move before this could have been Bh1+ with discovered check from the rook, followed by Kxh1. But with all eight pawns and the light-squared bishop on the board, that's also not a valid solution. I guess that explains the presence of the light-squared bishop in that puzzle.
BTW, einstein_69101, I just realized the idea you had in that position...white's last move was definitely the double check Nh6+ (or Nxh6+ if it was a capture); but there is no way to reach the position before that move because any square that Black's pieces could have come from puts either one of the kings in check (plus the c-pawn could not have come from b7 or d7 as there are pawns there, while it could not have come from c7 as the dark-squared bishop is on b8). Putting the extra pawn on h5 prevented the use of a black queen or rook to lose tempo along the h-file (pawn, bishop or knight were already invalid options in the original position as there are no squares they could have come from), so the position is no longer reachable. Quite a slick puzzle, nicely done.