Title should be QGA, not QBA. Whoops.
I'm not sure what went wrong. Was I just being greedy taking the rook?
From what I've seen and read, I played the opening well but I ended up being vastly underdeveloped and black was able to come back and regain his loss of material as well as launch a better attack.
I dont think you were losing at any point.
you were up a whole rook. so how about 9. Qg3 challenging black's queen to trade or to move to an inferior square.
I did not understant 11. fxe4 helping your opponent and ignoring your own development. you could develop another piece with 11. Nc3 instead, for example. in case its harrassed by 11...b4 the night can land on a4 followed by c5 later on.
16. g3 is questionable. 16.Be2 followed by castle short. black is down a rook and has nothing for attack.
I was winning in points, but positionally I thought that I was far behind.