You can trade pieces before the game
WHAT a FLOP!
How much experience do you have with chess? Most people start playing with a much lower standard of play than yours. Aside from your last move your only big blunder that I could see at my meager skill level was move 12 and 13 both of which lose material.

3.Be2 was passive; Bc4 and d4 are the more usual moves here. 12.Nd5 was a blunder that cost you a piece. Rad1 or f4 and f5 were better tries.
You didn't play badly, other than those moves. Maybe your nerves got the better of you?
(I'll resist saying "Ladya, you got rooked.")

*blush* Thank you! Come this August, I'll have been playing chess for 2 years. Come to think of it, were there actually 3 defenders on the f6 square that had the knight on it? That was what I was trying to obtain when I made the 12. Nd5 blunder. On second thought, how COULD there be 3 defenders on that square? There are the g7 pawn and the e7 bishop, so what happened? I was attacking Black's knight with both MY knight and my bishop. I shouldn't have lost any pieces there...
When you took his bishop you gave him the opportunity to both retreat his knight and recapture your piece. If you took his knight with your pawn instead you would have traded bishops and lost a pawn.
Come this August I will have been playing for 1 year so you have been playing for one more year than me.
So, I played my first game here on Chess.com with a friendly greeter, rodney1, and made a complete fool of myself. This is not what I intended to do...
All I wanted to accomplish was to trade pieces after the opening, and then my whole game fell apart. What went wrong here? I feel so dumb...
http://www.chess.com/echess/game.html?id=46077193