How do I identify strengths/weaknesses?

First off, drop this idea of being terrible at chess. No one is objectively terrible. There are thousands of people who you can crush effortlessly and thousands who can crush you effortlessly, and thousands who can crush those people effortlessly. We're swimming in different pools with our peers who are roughly equal to us. Second, you don't have to be good at analysis to analyze. Go in, make observations about your play. Be wrong, it's okay. As long as you are really looking and really being critical about it, you're doing yourself a favor and working toward improvement simply in the way of self awareness. When you've finished your own self analysis, get the engine involved, see where you went wrong in your analysis and really try to understand what the engine is telling you. If you don't, guess what? You've got an entire game that you've analyzed and annotated that you can now post in the game analysis forum along with your uncertainties and people will respond and give you feedback on you game and your analysis.

I know how to checkmate with single rook and single queen already granted, I'm kinda sloppy when there are actual time controls involved but I can still do it.

If nobody is terrible at chess, then nobody is good either. You can't have one without the other.

There is one important problem with that approach though. Up until a high level of play, it's hard to understand computer suggestions. Why is a certain move good? Quite often it's completely down to this exact position. So you run the risk of learning from the computer that a certain way of playing is good, while in reality it's bad, unless you're in that exact same position again where there is a deep tactic that makes it all work. Secondly, a stronger player can discard engine suggestions much more easily. I can look at a line and know it's unrealistic to expect to find that idea in my next game. At a lower level that's much more difficult. That's all why analyzing with a computer can do so much harm to a lower level player. It's much better to focus on general principles and try and work from there. 

#24
"You mean focusing on openings first, then midgame, then endgame?"
++ No exactly the opposite: endgames first, then middle game, then opening.

"I know to look before making a move so I don't hang any pieces"
++ If you consistently check before you play, then why do you still hang pieces and pawns?
The point is to split your thinking into two parts.
1) In the first part you identify candidate moves and you evaluate their consequences and you decide which of these moves is best.

2) In the second part you imagine your intended move played and you consider it through the eyes of a patzer: what checks / captures / threats my opponent has after the move is played?

Only if the check of part 2) is OK play the intended move from part 1).

#33
"In order to improve your game you must study the endgame before everything else;
for, whereas the endings can be studied and mastered by themselves,
the middlegame and the opening must be studied in relation to the endgame." - Capablanca