@Sarg0n Concerning the last puzzle:
1. a8=R Kh1 2. castling with the king going to c1 and the a8 rook to d1?
That's indeed an interesting question, how "moving two squares towards the rook" is to be interpreted when they're neither on the same rank nor the same file.
Rather than giving the player a choice and making the notation even more complicated, I'd suggest you simply have to move in a straight line towards the rook, for a distance of 2 squares.
So, for white, castling with a rook on a8 would let your king end up on approx. d2.7 .
( d.00772 2.73649 to be more exact. Even if it wasn't for the checkmate, this would be a great move. Just think about how save it is there! How to even check a king that's sitting in a weird superposition between the squares d3, d2, e3 and e2?)