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White to play and win

1. g4 h4

It's Black's response to 1. g4. It's up to you to determine if it's a refutation.

You are right.

h4 should be the main idea in preparation for g4 and a forced capture, but the there is ...f5! causing trouble for white. the the best move is to block that pawn push first with 1. e5. That is the winning move..

After 1..h4 2.g3 this will be a forced capture and the pawn will be unstoppable

sorry i edited my last post

1.e5 Kb4. Whats next? Or is it drawn?

e5 Kb4 white still wins by playing h4 -->g4 black can go the opposite board but gets stucked guarding the h4 pawn and white can gain time taking all pawn pushes from black. if the king moves then the whites pawn promotes.

But black takes the pawn

white wont actually need to go after blacks pawns, just need to wait for their push because blacks king is in zugzwang

Dude!!! Not hxg4, but Kxc4! If gxh5 then black king can capture white pawns, even e5.

This is a simulation of the moves both pieces can try, eventually white can win. 

You need to show what happens if 7...b4 instead of e5.

what exactly is the next move by black after 7..b4 8.Kb3 ? Do you want to push your pawns slowly or alternately like 8..b7-b6 /..b7-b5 / ..e5 either ways white king will just wait there to snap the pawns you push, will not actively get to the pawns but wait til you push.

Black's next move will be to call the TD and claim White made the illegal move of his king from d2 to b3.

there isnt any move that shows white's king jumped from d2 to b3