How to avoid a draw in this game?

I have two questions:

1) Was there a better way to play that endgame before the last four pieces on the board finished the draw?

2) Is there any way to escape that king knight situation that was occurring, at the end while I had my final pawn, so that I could have defeated him?

You forgot the link, Mr. Smart ;)

http://en.lichess.org/Jbqn58xKHncZ

Ah yes. That would be important XD

I'd say you were very lucky to draw that.
I'd understand you question if you were winning somewhere and lost the initiative, but this isn't the case here.
Be happy with the result and move on :D

There's normally no way do draw that, white has a too big advantage.

you are lost with 61.a6

I don't think it is possible to stop a horse from getting your last pawn in any case. (If it is just King+Pawn vs King+Horse)

ah, my eyes. make it stop. ok lets just forget everything... As for your question: pawn on the "h" or the "a" file and king versus lone knight wins if the pawn can carry itself to the 7th rank, if the knight manages to control it before that, its a draw.