I recently just lost a game against an odd opening I've never seen before, and I'll have to admit, it left me pretty flustered. Was the game ever a foregone conclusion? Did I screw up in the midgame by exchanging so many pieces, or in the endgame by hanging my rook? I'm a beginner, so I'd appreciate any thoughts/suggestions for improvement!

Black was controlling the center through "fianchettos," i.e., putting the bishops on the long diagonals and picking off your pieces and pawns that control the center.  It's part of something called Hypermodern defences, eg. King's Indian, blah blah blah.

1. ...e6 is designed to protect f7 from attack from white's light square bishop.   Unfortunately, 2. Bc4 attacks what is already strongly protected. Maybe consider attacking the initially unprotected dark squares instead.

I'm afraid I'm not the best person to tell you how to deal with fianchetto openings.  I think 1.e4 e6  2.d4 gives you good cover in this game (and *generally* in games in which you are confused about black's opening.)  Then develop your pieces normally.

Hope this helps.  :)

i just think you did not do enough thinking,

Losing the knight to try and go for the queen trade was stupid.