So yeah, broke my losing streak (even though I mostly played e4 in those games too). I think I'm still getting the hang of this particular opening and its variations (though I couldn't put a name to any of them). So I'll just ask for the usual critique and review, something I always find helpful

Mmm I agree... your advice has been well noted! I've noticed a tendency in myself to postpone taking pieces to guard against infeasible (is that a word?) threats. It's time I stopped that.

For your rating, that was pretty good

Well, that is a legitimate tactic in some cases. Called an intermezzo or zwischenzug where you can simply insert a move before the obvious to gain an advantage. In others (like this), you simply fail to take advantage of winning a piece and the chance disappears.

I'm a Petroff player, 4.Bd3 and 5.c3 is fine, that's book theory.

Although fine doesn't mean it's the best, 4.Nc3 is definitely what I would choose since it follows one of the general rules of the openings: develop knights before bishops.

7.Bc2 is a bad move, once again, because it doesn't follow the opening rule: don't move your piece twice in the opening.

9.Ba4, even if the knight wasn't hanging was also a bad move, 1. because it doesn't follow the mentioned rule, 2. because your pieces are disconnected and your attack doesn't look to have any plan. You generally want to pressure a chosen place and positionally or tactically gain advantage on one or two squares and when you have it, attack.