My First Self-Analysis
I think publishing your own analysis is a great way to try and increase your chess understanding. And it shows that you're serious when you post one of your losses! Here are a few thoughts about your game.
I don't see any reason to play 3.e3. Your d-pawn isn't threatened in any way, so there's no need to defend it, and 3.e3 locks in your Bc1. The most usual move in this position is 3.Nc3, which continues your policy of keeping the pressure on Black's d5 pawn. 3.Nf3 is also popular.
I also don't care for 5.b3. Why not 5.Nf3 developing a piece and preparing to castle? But I don't agree with your fear of giving Black's Queen a "powerful position" with 5.cxd5 Qxd5. After 6.Nf3 (to prevent Qxg2) and then 7.Nc3, the Queen will have to flee and you will have a substantial lead in development. In fact, Black would almost surely reply to 5.cxd5 with exd5 keeping a pawn in the center.
7.Ba3 is a bad move for all the reasons you cite, but it's actually even worse. As you noted, the exchange of Bishops leaves your Knight badly placed on a3. In fact, the Na3 is undefended and Black could have won a free piece with 9...Qa5+
It's no crime to overlook the deadly 11...e4 this time, but don't let it happen again! I'm just kidding, of course, but you should always be alert to the potential "forkability" of a Bd3 and Nf3. This threat comes up reasonably often, so you need to be alert. Yor pinning defense with 12.Re1 was a good idea, but it shouldn't have worked. After 12...Be6, you're losing material.
I hope some of this helps
Thanks, I appreciate all that a lot! Shows me some of the stuff I missed in my sleepy stupor :) I know I made some awful mistakes I don't usually make in this game, I figured it'd be a good one to look over to prevent future blunders.