English Opening Question - Please Analyze

So we can't look at the rest of the game? (what's wrong with 11 Qxa8 btw?).

I'm not an expert on the English--I've only played it about 10 times OTB, and I didn't learn anything to do it, just played it like a Sicilian Dragon. That said, I don't really like 4.e3. You already have a hole for your light bishop, and e3 blocks in your dark bishop. I would play d6 (to prevent any ideas of e5, and to let my dark bishop out), followed by Bg2. I would be thinking about maybe pinning the knight with Bg5, followed by Ne4, depending on his response. Otherwise, I might just finish development with Nf3. Hope this helps

This must be in an opening book or something somewhere...

a3 and e3 are book-ish moves in the english responding to Bc5, the idea is you get to play d4 (or b4) with a gain of time... but usually black has already played Nc6.  I don't think this matters though, e3 as played in your game is a reasonable response for the reasons given.

The opening moves in this game look standard enough.  Bg4 by your opponent looks off, Nb4 is premature, and your Qb3 is odd as well.

Did you try looking it up in the Game Explorer? Offhand I'd start looking at games with the most popular move played or better yet, stop playing positional openings like the EO altogether and start learning the basics starting with Open Games ie Double KP Openings whenever possible. This isn't my idea it goes back to GM Richard Reti's advice from "Masters of the Chessboard" who advised beginners to learn open games first, semi-open games next and closed games last.

Move	Games	White Wins Draws Black Wins
4.Bg2	176	40.3% 33.5% 26.1%
4.e4	9	22.2% 44.4% 33.3%
4.e3	1	Zarco Jose (BOL) - Radhy Sol (1978.??.??)