Sometimes playing to see what pawn structure the opponent is angling for is a good strategy.

This move can't really be bad, exactly. It can lead into a King's Indian Attack.

White having fewer pawns in the centre makes them easier to strike at? Something's wrong there....

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There are no drawing variations below the rank of master. Paul Morphy played the exchange variation of the French all the time and rarely allowed Black to draw. One thing the exchange variation isn't, is slow moving. Rapid development and the initiative are the keys for both sides. It is true that the lack of a center and symmetrical pawn structure can lead to a drawn end game. One of the worst things either side can do is think this is an easy draw and allow the other side to obtain the initiative.

In the Exchange French development becomes a priority. Moves like ...c6 are too slow.

Exchanging on c6 also came into consideration. Although the slight disruption to Black's pawn structure is only a minor inconvenience, it does create some kind of imbalance that White (and Black, of course, with his bishop pair!) can work on, come the endgame.

If he had done that, I would have aimed for ...c5 to dislodge White's central pawn.

Possibly, white is reasoning that this way he has a tempo to play a3 if black plays b5 with the intention of going on with b4. On the other side, if black goes with c5 (a sac that can worth a look), the bishop is already covering the good diagonal, that will become free sooner or later. The fact is that white is already showing to have lost the initiative.

I have a feeling your subconscious was yelling at you that there was something good in this position, but your super-conscious was being obtuse. Has happened to me a lot! At any rate, as you observe, 18...Bxf3 was fine for Black. Equally good would have been 18...Nxh3+ at once, with the idea 19.gxh3 Bxf3; or 19.Kf1 Bxf3! or 19.Kh2 Bxf3! with advantage to Black. Reconsidered your views on this "boring" opening yet?  

Yes. It's annoying for me, really: I spend all that effort livening up the position, and by the time I succeed, and get a strong attack, well, I blunder as follows:

Now that's what I call making a dull position more exciting!

Now, 22.Re1 and Black could just about resign...

White would have retained a large advantage had he been prepared to give balck the Queen; 23.Qxe2 Nxe2+ 24.Kf2 Nf4 25.Rd2 - protecting the b-pawn, and preparing to redeploy the bishop. The exchange plus would have given White the advantage.

Isn't 24.Kh1 better?

Indeed it is: and White would still have stood to win the game. White's choice of King move (24.Kf1??) is the second turning point of the game!

The only possible move was 25.Qa1, but Black gets much the better of the ending after 25.Qa1 Rxb2+ 26.Kg1 Rg2+ 27.Kf1 (Not 27.Kh1 this time, as 27...Ne2 mates next move) 27.Rxa2+ Kg1 28.Rxa1 Ne2+ 29.Kh2 Be6 and Black has too many pawns for White to cope with.

You've got mixed up there. 27... Rxa2 and 28... Rxa1 are Black moves, so White is to move next before your 28... Ne2+.

Just a comment for white: I feel pity for him. Can you imagine how frustrating can it be to win a queen for a knight... and lose the game???? Poor white!