What questions should I ask myself to determine my playing style.

Sure. Me first.

I don't own a single opening book... neither a book specific to a single opening, nor a general opening reference text such as MCO.

I own games collections... Zurich 1953, Karpov's best games, Alekhine's best games, that sort of thing... and a few strategy books such as My Sysyem, Chess Praxis, Pawn Power in Chess, Pawn Structure Chess, etc.

You shouldn't read Nimzovitch until you are Class B or better.

And don't read Alekhine at all. Just don't. He won't help you. 

Kmoch''s Pawn Power? And I'm getting heat for pushing opening preparation? 

I'd need to lose a few rating points to reach class B. Perfectly do-able, of course.

And after you've read the Nimzovitch, it will take you a clean year to purge him out of your system. Overprotect indeed. I think it was DeFirmian who talked about everyone's "Nimzovitch period" which is like some ritual scourge...but then has to be dusted away, like webs in the attic. 

Next time a beginner wants to learn, I'll remember maskedbishop -- here's how the pieces move, pawns are weird, but they can promote, capture en passant, this is castling... and here's Avrukh, memorize it now.

Jeeze... that's news to me. I played the best Overprotection game of my life only a few months ago, here on this site.

Check out the position on move 25.

I'm only an Intermediate player, but I think this whole "learn your openings first, boy or else you'll get in big trouble in your games." Is nonsensical. Not even once In my chess career, have I tried to even grasp those opening books back in my school library. You see, in the opening, all you need is a good understanding of the chess principles, and you're pretty much ready for the stage already.

Then the tactics, strategy, middlegame, endgame all come in and that's what truly makes a strong player. Honestly, do you actually think that someone, who has studied both the tactics and endgame vastly, would fall prey to some simple trap in the opening? Don't make me laugh, opening-"expert" intermediates (Actually, opening-memoriser intermediates). Focus too much in the opening, and you'll severely stunt your chess growth.

Most chess games from the beginner-intermediate levels are decided by tactics. So rarely that a game is won by outplaying your opponent strategitically...and so rarely, that a game is won by outplaying your opponent in the opening.

I'll try to get back to the OP, "what questions should I ask myself"?  To that point I think the 1st question is... am I passive or aggressive?  One should have enough self-awareness to answer that question honestly.

If Aggressive, then as White you should adopt 1.e4 and be prepared for anything.  If Black, then the Sicilian against 1.e4 and against 1.d4 well there are lots of choices but I think the Nimzo-Indian or Benko Gambit is a good place to start.

If the answer is Passive, then as Black against 1.e4 I think the Caro-Kann teaches subtle defense.  Against 1.d4 then the Slav or Semi-Slav follow the same vein.  Of course as White the choice is 1.d4.  Queen pawn openings teach a slow build up of one's pawn structure.

So, ask yourself...  are you a 'bare-knuckle brawler' or a 'connoisseur of finesse'?  If you're honest with yourself, then the answer should point you in the right direction of openings to study.