Is this position legal?

Ah, for some reason it didn't occur to my mind to retract a capture that is not forced.

Is this legal?

Trivially. Last move was Nany-e3#.

The last one posted, of course, post #1160.

#2 is legal.

1.e4 Nf6 2.d4 Ng8 2.Nc2 Nf6.

lol.

Is this legal?

That one is crazy. My guess would be yes but who knows.

Given the king positions, I'll say illegal.

After working on your last slew of positions, the cage here is very familiar.

My answer's no, it's not. Even if white were missing the b1-knight, it'd still be illegal I think.

Yes, the cage is almost the same in some parts. It's pretty much another variation.

Here is a simple position, feel free to solve. Is this legal or illegal?

Yes.

Correct, the 5th variation from my last thread had this theme (with the pawn being captured), only there it was illegal due to other concerns.

bRa8 is caged, so one of the black Rooks on the board is promoted. It had to be the h-pawn. Thanks to Bh2, the white g- and h-pawns did not cross-capture. The h-pawn could only have promoted by ...hxg3 and ...gxh2. Those are dark squares, as is f6. One of white's missing units is a light-square B, so white cannot supply 3 sacrifices on dark squares. The position is illegal.

#1168 - I say not legal.  Unless I overlooked something:

White's last move must have been Rook from b5-b4+ leading to the double-check.

Black's previous move must have been the e pawn from e7-e6 (I don't see any other legal moves for black).

Going back to White's previous turn, I see no legal moves.

EDIT - White actually could have moved c7xb8 and since one of black's pawns could have promoted it technically can be any piece on the board (not necessarily a knight, which would have been illegal since the white king would be in check).  But even then I cannot see a legal move for black going back one more move, so the conclusion is still the same.

EDIT - Just saw BigDogg's answer - very impressive!

This one is probably too easy for you. Anyway, I wouldn't say hxg3 is forced, because it isn't, but the h pawn can't capture white's last square bishop until g3 is played. At which point, the pawn must be on h2, having captured both knights. This leaves white with his light square bishop for exf6, which is indeed impossible, as you say.

Here is another simple position (you might recognize this theme as well, BigDogg). Legal or illegal?

#1178 - Legal.  Black king could have gained entry via d3 (before d2-d3) f3 (before d2-d3, e2-e3 or g2-g3) or h3 (before h2-h3).

Ahh, but what about Bc1 reaching h2?

Damn you're good. Missed that.  :-)