Hello
The analysis I think is better than I would do on my own work. The only problem is the wording mixed in with the notation for some reason, and messed up my syldexia. I fixed to so I can read it and comment better. Notation is below, your wording is untouched. I will place my remarks below yours.
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1. d4 d5 2. c4 e6 3. Nc3 Nf6 4. Bg5 Be7 5. Nf3
{Queen's Gambit Declined.}
I would worry less about openings and more about logical moves. (This is new advice from someone I spoke to recently.)
.. c6
{A sort of pseudo-slav move.}
I would imagine it would be more of a regular slav move. What makes it Pseudo?:-)
6. a3
{To prevent complications after 7. e3 Bb4 8. ... Qa5. I tend to avoid those types of lines.}
Point 1: This may have been mentioned before but to get better you want to learn real openings and go in to them even if they hurt.
Point 2: If you think about this position logically, you wouldn't be thinking about this line. In the opening Tempo is very important and him playing Bb4 after playing Be7 would be silly. Basically admitting that Be7 in the first place was a mistake. For example: He could have went 4. .. Nbd7, which is a "sound" opening trap. You should have questions about it, try figuring it out.

Give yourself about 30 minutes, if you can't finger it out ask here. The real strength in this move is it develops a piece and namely a knight and holds off developing the bishop a move to see if you want to go into the Bb4 ideas. It's much better in this case. Granted this might be trivial, but it's very important to notice small things like this. YOUR development and YOUR plans are more important than his. Unless he has real threats against you.
..o-o 7. e3 Nbd7 8. Qc2
{Setting up for the typical e4 push.}
..h6 9. Bxf6
{Black's knight was better than white's bad bishop. In addition, if white plays c5, black's dark bishop
will have limited scope of movement. This would probably be preceded by b4.}
I don't know if I would agree that the knight was better, but to trade here could have been thought on more. It's probably correct because usually when you play Bg5 you are set out to take the knight when challenged. The thought that the bishop was "worse" than the knight in that position is probably incorrect. In my opinion, you are the one with space advantage so you are the one that does not want to trade. Possible Bh4 was better, several factors are in on this. One of them is he is castled and you are not. Making the decision to chase you with g5 a little crazy.
..Nxf6 10. Bd3 dxc4 11. Bxc4 Nd5
{This move is probably a little hasty. The
knight can be kicked off of the outpost. White has several choices: e4, NxN
and O-O. I rejected e4 immediately when after 12. e4 Nf4 O-O Bh4 followed by
Qg5 black has some kingside possibilities. NxN is bad because after exd5 his
light bishop is freed, e4 is prevented and white loses a tempo moving the
bishop. Thus I played O-O prior to beginning central operations.}
Not hasty, just not good. 11. .. c5 is better here in my opinion. Black may win this position but he seemed to play poorly in the opening and wait for you to make a mistake. Which worked, so he learns nothing.
12. O-O Nxc3
{I think this is also a strategically poor move by black. The knight
was black's only active piece. After the exchange white's pieces are better
positioned.}
I completely agree with this. Again 12. .. c5 here may have been better.
13. Qxc3
{Probably better was to take with the b pawn, and
use the rook to pressure the b file. I felt that the rook pawn would be
vulnerable if left alone, so I took with the queen. This move had
ramifications later in the game.}
The move you said is probably better. I think that something you should be thinking about is where your pieces belong. One thought is: Where do your rooks belong?
.. Bd7
{Black spends several moves reorganizing his pieces.}
Poorly Organizing his pieces. Remember, he wants to fight for the center. He is not doing this, your gaining in power.
14. e4 Rc8 15. b4
{In order to allow the queen's rook to get into the game.}
This move probably deserves an exclam if it were not for your move 16.

..Bf6 16. e5
{Although this creates a backward pawn on d4, I felt I could sufficiently protect (overprotect) it.}
This I feel is a bad move. Because your wasting time and giving him ground. Think about it this way. YOU want control of the center. So where is that? e4 d4 e5 d5, right? Well a move ago it was white who had control over these squares. Moving to e5 might seem like an aggressive move to push him back but it gives black the d5 square in return for your aggressive intentions. You might gain space in return, but I don't think it deserves the weaknesses you created in your own camp. A much better move would have been to play Rfe1. Also look at the pawn structure. VERY important. This is actually a Caro/Slav pawn structure. More specifically a Slav pawn structure, which you kind of denoted in the beginning. So what you want to know is: What are the plans in this pawn structure. What you might find out is one of the plans are to push the d5 pawn to break open blacks center.

You just ruined that possible plan. I am still reading and learning about this so I am no expert by no means on the subject of pawn structures. But simple ideas like that could help in the long run to tell you when certain pawn moves are bad. From the book I am "trying" to battle through the main example of this plan is played by Spassky. He is a very good person to learn from, so one of my suggestions might be to search for games played in this pawn structure in a database. If you have Chessbase 8 or higher you can do searches on pawn structures. Just do the search, and place the pawns on the squares you would see them in the structure. "JUST THE PAWNS". You might have to monkey with the positioning of the pawns, like placing the a3 pawn back on a2, or placing the h6 pawn back on h7. Minor things. And just do a search on the pawn structure. Look for "Spassky" games first. Then look for games by players above 2600. If you do this and have questions about the games feel free to send me a message and we can discuss it.
..Be7 17. Rad1
{Continuing to build central pressure and minimize the scope of the black
pieces.}
..Qb6 18. Kh1
{In retrospect, probably unnecessary. White had ideas of f4 and Rf3-g3 with strong kingside possiblities.}
In this position yeah unnecessary. Funny enough but because of your "e5" and ideas of f4 and Re4. The best move could be Nd2-e4. Take a look at that possibility and see if it looks good to you. Knights are great attackers in closed positions. Never take your eyes off of them. (Watch all your pieces of course.)
..Rfd8 19. Rfe1 Be8 20. Re4
{With plans for Rg4, Qd2 etc. Unfortunately these never get off the
ground. At this point white's plan is to use the d4 pawn as a sort of bait
with which to occupy the entire black army, then quickly shift over to the
kingside for attack. As it turns out, black is able to create a weakness and
break through in the center.}
In retro: You should think of it this way. Was it black or white who created the weaknesses in the current position?
Every move creates a weakness, it's up to the player to decide what and where to create those weaknesses. If you start creating less weaknesses, as you get stronger you will find out how your opponent will "Create" weaknesses against you.
I will stop the analysis here. I thought the rest of the game was interesting and the analysis was great, but I also think this is where you would learn the most at this time.
Hope I helped, and remember this is just my opinion. I suggest getting more opinions to supplement the possibilities.
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.. c5 21. bxc5
{As cxb4 would be unallowable.}
..Bxc5
{This move I did not see coming. In placing my rook on e4, I
inadvertently left my d1 rook undefended and pinned by a pawn.}
22. Rde1 Bxa3
{Black breaks through, and the c8 and d8 rooks become very strong very
quickly.}
23. Qxa3
{White seeks to simplify and attempt to regain the
initiative.}
..Rxc4 24. Qe7 Qc7
{Here as white I desperately searched for a
possible continuation on the kingside, but time trouble was beginning to
creep in. I began to play for a draw.}
25. Qxc7 Rxc7 26. Ra1 a6 27. h4
{Creating luft, and beginning the process of putting the pieces on dark
squares to avoid blacks bishop.}
..Rdc8 28. Ree1 Bc6 29. Kh2 Bd5 30. Ng1
{Black's bishop cannot be allowed to remain on d5. The knight is bound for
Nf3-g1-e2-(c3 or f4 depending).}
..Rc4 31. Ne2 f6
{An error by black. Here black is opening up a file for white's e1 rook and breaking up his kingside
pawn structure.}
32. exf6 gxf6 33. Rad1
{To allow Nf4.}
..Kf7
{An excellent positional move that prevents Rxe6 or Re7, and places the king closer to the
center.}
34. Nf4
{Still trying to trade pieces to try for a drawn rook ending.}
..Rd8 35. Nxd5 Rxd5 36. Rb1
{Offering an exchange of pawns.}
b5
{Naturally black does not accept the ludicrous exchange!}
37. Ra1 Ra4 38. Rxa4
{Probably best would have been Rd1 where after RxR RxR white retains
pressure. If Rxp RxR RxR Rd7+ Kg6 Re7 white is still alive.}
bxa4 39. Ra1 Rxd4 40. g3 Kg6 41. Kg2
{Keeping the kings in opposition.}
..e5 42. Kf3 f5
{Here I was a bit confused. I had expected black to march his king over to
the queenside and push the a-pawns.}
43. Ke3 Kf6 44. f4
{If pxp KxR, etc. White hopes for pxp Kxp and some possibilities with the black king in the
center. (These types of endings are one of my main weaknesses).}
..Rb4 45. fxe5+ Kxe5 46. Ra3
{Crafty (score -11.17 at depth 12) thinks this is a
blunder}
..Rb3+ {Whis resigns. I was relatively proud of containing my much
higher rated opponents pieces in the opening and middlegame. However, the
transition from middle to endgame could have been played better by both
sides, and a terrible blunder left all my effort for nothing. This game was
a learning experience.} 0-1