I'd appreciate some analysis of this game - where exactly did I (playing black) go wrong? I believe taking the pawn on move 16 was an error (although the ~2500 chess.com computer didn't give label it an error), but I want to take away more from this game that just "Make sure your queen doesn't get trapped". 

WT weaken his d4-square with 6.e4?!. This is a dark square so you can use your dark bishop to put pressure on this square. But what you did is exchanging the dark bishop (7...Bxc3?!) causing WT's pawn on c3, making d4-square no longer a problem for him. Plus I don't like giving away bishops when still complete (as this creates possibility for double bishop) without compensation. And I don't see the doubled pawn as a compensation.

After the last bishop exchange on move 9th, WT perfectly had a double bishop and a strong center. I'm not sure this is a closed position as WT's center pawns are free to advance and open up position. So WT should have not closed the position with 15.d5?! (rather WT should have maintained tension in the center while developing in the back rank such as releasing the f-pawn), after which I prefer BL position for the Knights superiority, with c5-square as a good outpost for the Knight.

Your effort to capture the a-pawn (16...Qxa2) reminds me what a coach used to say to his students: "You want more pawns? Go to my home. I have plenty of pawns in the toilet!!". I don't know if there's anything else to analyze/evaluate after the Queen's "brave" action (as it is now tactical).

I always play the english as white, love it when black plays Bxc3 against me as they get rid of a decent bishop, and give me an open file for my rook. Yet to understand what makes that move so appealing for black, the doubled pawns aren't much of a problem.

Move 15, I may have kept queen there, and looked at attacking the dark bishop with the knight, or perhaps look at pressing the d pawn. Whites pieces are all on kings side of board, sending queen off to attack that one pawn didn't give you any advantage imo