I would play this as almost a sac of the first pawn. White wins and no draw. Starting with Ka6.
Puzzle #2

This is a draw! The black king always goes on opposition to the white king (check rules of opposition). Black will lose its pawn but even if white keeps both of its pawns, it's impossible to win because black will manage to hold the opposition.
Azul, it's not a draw (but when I first saw this, I had to stare at the board for about 35 minutes to find the solution).
If you're familiar with the concept of related squares, it might help.
I took the liberty to post this very simple endgame puzzle, exactly for its simplicity. Now I don't like the idea of posting it as a puzzle, as the analysis of different ideas (rather than a single answer) is the point of it. So here it goes: