Question: stalemate with king vs king pawn

It's drawn if the opponent's King is in front of the pawn and also if they can trap your King in front of your pawn. If "my opponent is in front of my king", then it depends what you mean by that (not sure if you had a typo there).

@jialeming, If you want to win that, you have to be able to prevent the opponent's King from getting in front of the pawn (they can just stay on the h file forever) and also you must prevent them from reaching the critical square f8 (if they get there, they will either get to the h file or the will be able to trap your King on the h file where it stands in the way of the Pawn).
White wins:
Draw:

With any non-rook pawn - including the king pawn - whether the pawn promotes depends on the relative position of the Kings - see, for example: https://www.youtube.com/watch?v=v5HBtQ7KHNo
With any non-rook pawn - including the king pawn - whether the pawn promotes depends on the relative position of the Kings - see, for example: https://www.youtube.com/watch?v=v5HBtQ7KHNo
that is very true