like i said, nowhere near the best line :P will change that to something more suitable

in your red line, instead of 14 kh4, white could play Nd8.. that will be at least a draw for white..

I will add to the red line which is if he doesn't take the pawn

Move 4 (see your brackets, but without kxh6, would your position still be better?)

on which move do you mean that the king goes to h5?

nice!

Small remark.. what would happen if the king went h5.. Rg8.. but without him taking the pawn (thus no mate), would you still be in a better position??