Looks like your opponent did OK. On thing is that the Kg2-g3 is jsut a waste of time since there's nothing happening on the K-side. Your "kind opponent" should have run his king over to the Q-side asap to help hold back your pawn and certainly not allow your king into d5 (that's the counterplay killer for sure!). At the end, after a little work with Deep Rybka 3, it evaluates at -0.67, but I think white will soon run out of moves and the evaluation will scream downwards in black's favor.
No, that's not a deep line suggesting better play, but maybe it gives you some general ideas of what better play might look like.
Best,
ZV
Here is a game I recently played and won in, IMHO, a decent endgame. The win was secured, IMHO, not later than on 24...Rxa8. I am interested if I am not seeing a better play for white (resulting in at least a draw), starting from 25.Rb1. Many thanks in advance for your input.