How could I have played better?

Please don't check an engine.

I would like help conceptually and perhaps tactically, not by a computer who just gives evaluation with no explanation.

 What is it with you and the hate of engines?  

Many troll topics get dozens of posts per hour, I post a legitimate chess topic and only get one response in 15 hours?

I agree with your note to your 20th move.   Hence White should play 19 f4 to control more of the Board to try and get a positional edge........could try to triple up on the "d" file.

I didn't check an engine. I checked a database.

This is a tricky opening, I'm not very familiar with either the English Opening or the Dutch Defense (this game mixes both!), and your rating is fairly high, so it's not surprising nobody knew what to say for this game. The database had only one game that matched this one out to 8. O-O, then it deviated with 8...Bxc3 instead of your 8...e5. A simplistic conjecture but one that also seems accurate per the database is that you shouldn't have played 8...e5. After that your pieces all seem to be in the wrong places, especially your queen, which is potentially in line with White's QB and QR. In the database game (played between two masters), Black attacked via ...Ne4, which prevented White from playing Bg5. That nuance seems to make a big difference, since that bishop pin Bg5 gave you a lot of trouble in this game. ...Ne4 and ...Bxc3 weren't easy moves to see, though, since they seem to violate various opening principles (viz., giving up the bishop pair unprovokedly, and moving a piece twice in the opening).

All of which goes back to what I mentioned earlier: Your rating is getting pretty high, you're on your way to master level, and my guess is that one thing separating you from the masters is that you'll need to consider such positional nuances more carefully. Anyway, the only database game that had your opening was also a draw (by repetition), so already your result is that of masters, so please give yourself a pat on the back.

I think 13...Bxc3 is more or less a blunder.

That seems like black's best piece that you are vapourizing.

16...c5 also seems almost like a poor choice since the rook moves to d6 and is now attacking your bishop on e6.

I would probably try to activate your a8 rook by moving the black queen somewhere maybe to a4 or maybe to g6.

Well yes.
The problem could be Dutch is not well known.
I liked 13. ... Bc5 because it pins. 14. ... Qh5 15. ... Ng4 16. ... Qxh2#
I was all excited about 25. ... Bd7 but thought Bh3, Rd1 etc made that weaken than the game move.
It was a pity ... Rxf3 was not available due to the mate thread on g7.

I'd rather not take on c3 unless white spends a tempo to force me to do so, or white has some unpleasant tactical or positional threat that Bxc3 defends against.>>

...Bb4 can be thematic but in my opinion you can take on c3 immediately, after which you can aim to place your pawns on the dark squares, which makes sense positionally. In the context of the moves played, ...Bc5 looks interesting. You might be able to push e4-e3. So maybe 13 ...c6, with the intention of Bc5. You shouldn't have swapped on c3 after the moves played, because your bishop should be more annoying to white than white's knight will be to black.

what stopped him from e4?

    You played pretty good.

  I think the only line that troubles me is your opponent didnt play e4.

  NICE CLASSIC

move #8 you retook and gained central control. 

     Your Opponents fatal flaw was moving his bishop to exploit a pin , and restored tempo in your favor , better was E4 winning the exchange with the center in their control.

  More discussion needs to made about counteracting E4

GM Simon Williams is probably the leading expert on the Dutch.  If you watch his games and/or videos, he says that Black is generally at least equal if he get pawns on e5 and f5 as you did in the game.  His games often feature a simple plan of Qe8-h5, as you show you in one of your variations.

Your decision to play both e4 and then Bxc3 just a few moves later is positionally dubious.  You advance in the center, creating some dark-square weaknesses ... and then immediately trade your dark-square Bishop?  Your remaining Bishop stares at your central pawn chain and is further blocked by White's c4-b3-a2 pawn chain.  e4 is almost certainly premature.

The correct middlegame plan, I believe, is to keep your central pawns where they are as long as you can while you maneuver your pieces towards the Kingside.  You can then play either f4 or e4 as the position dictates.  By playing either move too early, you rob your position of its dynamism.

That's my unprofessional opinion, at least.

At your level, you shouldn't be afraid of engines anymore. They can be useful for sorting out the details.

I can only agree with that. After Bxc3 you are positionally lost. E.g. in the game 20 f4 or 21 Qe5 both give white good (maybe winning) advantage.

However, white should not exchange his bishop on move 18, but either win the pawn with Bxh6 followed by Re1 or play Bc1, b3, Bb2 or Ba3 when black gets no counterplay at all.

As proposed above you must play 13 Bc5.

Productive learning