Hi Rockstar189--let's start from move 26 when everything but the rooks and kings had left the board. Those endgames are frequently drawn, even with an extra pawn on one side. You do have the advantage for a few reasons here though: white's kingside pawns are shattered, your rook is on an open file, and it's your turn.
26...f6 was a mistake because you don't need a turn to defend. You only have one pawn "island," or group, and it's easily chained at any time. For example you put your pawns on g6/h5, your king on e7, and look--everything you own is defended. White can't do the same because of that gap between his h-pawns and his other ones. So you wanted to immediately get your rook behind those pawns, stopping white from doing the same: 26...Ra2! sets up 27...Rd2 and your opponent has problems already. You came in from the side instead, which allowed white to defend with his own rook on f3. 31. Rf2?? actually lost for white after the rook trade, but the battle continued. It was mostly drawn after that, but you blundered the pawn on e5 and it went downhill from there.
So the problem was that you didn't really see your dynamic advantages. You followed certain principles of controlling the 7th rank, attacking stuff because it was there, etc., but you had nothing to worry about with your defense. The king could handle himself and your rook should've been finding its way behind white's pawns immediately. That would have made all the difference.
My late game/peon game is really weak, I almost always lose in an even game. What are some principles and/or tips to help improve in that aspect?
Sometimes I hold onto King safety for too long so after the dust settles and lots of material has been traded his peons are well advanced in comparison to mine.
Here's a game where I was way to focused on pushing my peon and got mated, but even before that I feel like he was getting the better of me in the even peon/castle game.
http://www.chess.com/livechess/game?id=778595583