Studies to solve :)

Three of my favorite studies.

Will you solve them?

That was nice.  On the second puzzle the bishop under promotion was misterious to me.  Thanks for the puzzles.

In the first puzzle, why wouldn't the king take the rook as soon as it moves to g2?

Well, this is the point of the study. Taking the rook immediately will not work. Try it out! :)

Spoiler:

With the pawn still on a2, the knight cannot stop the two queenside pawns in the end.

I get the first puzzle, but the bishop under-promotions baffled me

Just look at the position after white's 17th move, and imagine the pawn is still on a2.  That should help you figure it out

Take a look for stalemate tricks. 

In both the second and third problem, these are important defensive ideas.