Where did I go wrong? QGD loss as black
The exchange variation with Nf3 is harmless because can solve white square bishop problem with 6...Bf5 or possibly 6...Bg4. Don't think including h6 helps much. The point of h6, as I understand it is to follow up with Nh5, or if haven't 0.0, g5 then Nh5, to exchange Bg5, and get two bishops. (You did eventually do that on move 19, after a few not very to the point moves by both sides). The usual idea of playing the knight round to e6, is to follow up with g6. Ng7 then Bf5 to solve white square bishop problem. This is problembatic with h6, because Bxg6, and Qxg6ch could be strong. Other cases where h6, doesn't help is when play third rank idea with Re6 to defend c6, and to be able to play rg6, rh6 to support kingside attack. If that plan with Ne6 not viable then Nd6 is more often a better square for knight. Otherwise played a few pointless moves like bd7, it is arguably better on Bc8, and Bf6, were it was better placed on e7, if white plays b5, then bxa3 possible. Both sides "oscillated" for no obvious reason i,.eBe7, bf8, Be7 and Ne6, f8, e6.
It would help to learn the typical plans to face minority attack. For example a typical one is playing b5, then nb6-c4, with a5, and a5xb4.
TwoMove said almost everything and left us without job , lol.
7...h6 is not a mistake but it's not a prticularly useful move at this point and denies you many useful options(like a later ...g6 or a later ...Ng6).
The move order your opponent choose allows Black the chance to get a comfortable position with either 6...Bf5 or 7...g6 with the idea of 8...Bf5.
Another idea that can seriously mess with white's development if he is not careful is 7...Na6.
If white plays a3 then Black goes for a fast Nc7-Ne6-Ng7 manoeuvre.
After 19...Nxg3 20.hxg3 you are fine but you don't seem like you know what you want to do.You don't seem to have a long term goal.The additional problem of the early ...h6 was that a later ...f6 would create a terrible weakness on g6. So you should probably try to deal with that problem.
After that you played23...Ng5 and 24...Nxf3+ , an exchange that didn't offer you much especially if you consider how many moves you lost with that knight. I have the feeling that exchange wasn't only aimless(Nf3 was neither a serious threat or an important defender) but also a serious strategic mistake( a knight that moved 6 times was exchanged with a knight that moved 3, means you lost 3 tempo ,almost a pawn).Indeed the position becomes quickly difficult after that exchange.
Instead of the exchange ,maybe 23...Rad8 was a good idea and if white doesn't exchange on d7 you could follow with 24...Bc8(a manoeuvre Yusupov has played many times).
The standard way to counter the minority attack in the QGD is to counter with f5
I think black is guilty of generally timid play here. White had all the time it needed to set up the eventual queenside push (though the open h-file, especially after the exchange on f3, looked like a good line of attack, too.
Once you were down a pawn or two, you needed to get the rooks off, and keep the bishops on. He had 2 pawns on you, but one was a doubled pawn, a draw black should be able to hold.
It doesn't matter how good a defensive formation is, if you give a player of that level enough time, he'll usually find a way to pick it apart.
The standard way to counter the minority attack in the QGD is to counter with f5
I didn't know that. Thanks for mentioning this move.
You played very passively and gave your pawns away. 6. .... Bf5 obvious but it isn't necessary. But if you don't play it then you're trying to win, and were you good enough to beat this person?
The exchange variation with Nf3 is harmless because can solve white square bishop problem with 6...Bf5 or possibly 6...Bg4. Don't think including h6 helps much. The point of h6, as I understand it is to follow up with Nh5, or if haven't 0.0, g5 then Nh5, to exchange Bg5, and get two bishops. (You did eventually do that on move 19, after a few not very to the point moves by both sides). The usual idea of playing the knight round to e6, is to follow up with g6. Ng7 then Bf5 to solve white square bishop problem. This is problembatic with h6, because Bxg6, and Qxg6ch could be strong. Other cases where h6, doesn't help is when play third rank idea with Re6 to defend c6, and to be able to play rg6, rh6 to support kingside attack. If that plan with Ne6 not viable then Nd6 is more often a better square for knight. Otherwise played a few pointless moves like bd7, it is arguably better on Bc8, and Bf6, were it was better placed on e7, if white plays b5, then bxa3 possible. Both sides "oscillated" for no obvious reason i,.eBe7, bf8, Be7 and Ne6, f8, e6.
It would help to learn the typical plans to face minority attack. For example a typical one is playing b5, then nb6-c4, with a5, and a5xb4.
Exactly. He doesn't seem to know the basics of this opening.
After white goes for the exchange variation, you want Bf5 if possible. You also want to play a5 because then after white's move b4, you get the a pawns off the board, so even the worst case endgame is not a forced loss 
Also, as he more or less points out, you're mixing systems. h6 didn't makes sense in your game.
Another idea of Ne6 (other than Ng7 with Bf5 as he mentioned) is that Ne6 protects d5, allowing you to sometimes play c5.