Annotated below.

I thought 5...d4 was too committal. Black has more mobilization to do and I don't see the pawn move doing anything to help with the struggle. It doesn't matter if c3 happens before or after this move, and d4 certainly isn't something to fear as french advance lines with an early f4 are pretty harmless. The c3 knight can be 'denied' after it goes there for a tempo, too.

8...Qc7 is not the most active plan. The center is often the safest place for the king and black's defense must remain aggressive. a6 with or without b5 may be better as it starts to make the knight on a3 look silly. Perhaps another idea is to move the knight (a5? e7?) looking to exchange bishops and highlighting the problem with the central light squares.

9...Nf5 is unnecessary. 0-0-0 defends the pawn adequately and there is no follow-up plan for this knight.

After 11. Nc4 white is eyeing a potential outpost on d6 that could devastate your position. Nce7 is possibly the only move that actively helps this plan. Additionally after Nh6-f5 there is a common idea of following up g4 with Ne7-g6 and utilizing the weak dark squares. You have too many pieces and ideas based around e7 and it becomes easy for white to break your coordination.

Ng6 was a mistake but also a tremendous loss of opportunity. White has trouble with his central light squares and d5 is an outpost that dominates the center. Followed up with Bc6 and black starts to take control.

18...Nd5 and you're starting to utilize the light square weakness finally. You didn't get there in the ideal way but you did accomplish removal of the light square bishop and some central control. 

After Nd6 a substantial portion of your effords should have been directed at exchanging that knight. For the moment nothing is threatened but it is too well placed and can not be allowed to stay. Rg8 b6 (else white plays b6 and N4b5) and Bxd6 should be sufficent.

23...Qa5 further removes your queen from the center or king side, while it doesn't help with the queen side.

After ...Qb4 it's time to resign as white has material and good coordination.

At the time, my mind was wrapped around the plan of a pawnstorm, and how to work the pieces to support the advancing of pawns. I didn't fully consider the merits of ditching that idea (as well as my pawn structure) and simply pointing a rook at white's king with a semi-open file.

I thought that ...d4 would prevent c3 if played before, since ...d3 would block in white's bishop, and create a potential knight outpost. Perhaps I should have prioritized piece mobilization, though.

I agree that c7 was a poor spot for the queen. I don't quite understand the idea of exchanging light-squared bishops; wouldn't both sides have light-square problems as a result?

True, ...Nf5 made the knight look a bit static, since d4 was already mine.

When you mention the g4 follow-up after Ne7-g6, do you mean gambiting the pawn? I don't quite understand that paragraph of comments.

I originally discarded the idea of Nd5, since Bxf5 would make the knight lose its nice perch. However, I didn't notice the nice things that could happen after freeing up the file for a rook facing a queen.

I moved the queen only considering the idea of getting her out of immediate danger (but only 1-2 moves deep...), without considering using the piece to further my plans. In fact, I probably should've reevaluated my plans, then stuck with them or come up with something else to follow.

Thanks for all the comments, folks. I really appreciate them, especially coming from much higher-rated players!

The advanced d pawn is cramping, so while maybe not most accurate I don't think it was a bad idea either. It's certainly a valid way to play, my comment is more so that it's just not necessary to commit to such an ambitious plan. 

When the light square bishops are exchanged white is left with too few ways to cover the light squares. This will mean white must stretch to prevent your knights from penetrating, or that you can pivot on squares like d5 or e4 to control the board. The h1-a8 diagonal is weak for white and leads right to his king. Lastly notice that black has one of his central pawns on a light square (with the f pawn to support it), while white has none leaving e4 weakened. This could be exaserbated if black manages to somehow play d3. In general with color complexes it is more important to remove the defenders then to possess superior force on said color, provided your pieces are positioned well for those plans.

In many lines of the french the knight goes to f5 because black is equally happy with the added control of d4 or with inducing g4 to kick the knight. If white kicks the knight then it can maneuver e7-g6 (or a4 if you have Be7 played) where it prepares to access the newly weakened dark squares a4 or f4. 

While a knight on d5 would lose support if white plays an immediate Bxf5, it also becomes unclear how white could attack d5 to drive the undefended knight away after his bishop is removed. Fastest is for white to use his strong queen side knight which would be a major concession on his part (no longer would it eye d6), and he would need to do it from a square he doesn't mind recapturing on (Re1 then Ne3 maybe, since recapturing with the d pawn may not be desirable). The other knight is three moves away from d5 and also awkword to support. This gives you a few moves to figure out what to do with your knight or to advance your own counter-play.