Is this position legal?

Unfortunately incorrect; it could have been a-pawn that promoted.

Then tell me who captured the h-pawn? There are three captures made by white, namely the a-pawn, the h-pawn and the DSB of black.

Those captures are executed by the a- the d- and the g-pawn of white.

If the a-pawn was not captured by the a-pawn of white, yet the a-pawn was captured by the g-pawn of white. Who captured the h-pawn? The d-pawn or the a-pawn of white? That can only happen if the h-pawn was promoted as well. But after the a-pawn, because it must promote on the g-file. Therefor has the h-pawn captured the white bishop or queen.

I must agree, it is possible, but then do I have to admit that I don't know (yet).

No, I haven't tried that yet. I just checked your reasoning; the fact that you immediately declared "It must be the h-pawn" struck as odd for me, since you haven't proven it couldn't be the a-pawn.

Position #4 is illegal as for upside down pawn can't change files without capturing :/

Haha, I'm glad you like it. I also like your problem as well. Needless to say, when I am composing, functionality is of a higher priority than aesthetics, although it is quite nice when you do somehow manage to squeeze both in there.

You guys are giving me an itch to start composing again..

derp

#1267 is legal and a good problem. Not much freedom in the retractions until bKa4-a3 can finally be retracted. I especially liked the moves of the wLSB and the bN. I won't spoil it for others. The mate in 1 problem by Remellion is nice as well.

puzzle # 2 is most certainly possible. black just moves the knight back and forth

That was 13 months ago!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

I'm reposting an old creation of mine to entice more people to participate.

This one is quite easy.

Could white possibly castle in this position?

It is not possible.

Retro composers generally have a can-do attitude. The answer is almost never 'illegal' or 'not possible'.

^ Correct, I will post more soon.

Except when I fail at composing and the illegality is of course completely 100% intentional. :P

Legal or illegal?

Another very old creation (difficulty: easy)

Who can castle?

Black can, I think.