Hi (privet student),
Bellow is the endgame you sent me for analysis.
40.Qg4+,Ng5 note your Knight isn't forked since the Queen is protecting it. Therefor you can play 41..Kf6 (instead of 41.Ng5 loosing a piece).(41..Kh7? gets no where after 42.Qh3+, Kg8? 43.Qc8,Kh7 44.Qh3,Kg6 45.Qg4,Kf6 a few moves later since 45..Kh7 would lead to a perpetual check.
43.bxc3,Kf5-After all the pieces are exchanged with a forced variation we get a k+5p vs k+5p position. Blacks king is better centralised then whites, and that should prove to be a adv.
You asked about playing 43..kg4, instead of 43..Kf5 .
43..kg4 44.Kg2,Kf5 45.Kf3 - gives white a easier and better endgame compared to the line played in the game after 43..Kf5.
44..Ke5 -is a good move black can't hit the c3 pawn on time with his king, but he will have a well placed king and have control over the pace of the game.