french defense trying to trade off bad bishop

"There are only 5 master games in this position, because white already misplayed it." No, white did not misplay. It is just an unpopular line now. Nimzovich recommended it and played it several times. Alekhine played it. Short, Spraggett & Hodgson played it repeatedly.
"I was on the black side of this line bazillion times and can say that black has quite an easy play there." That is probably because your opponents misplayed it.
"I think like you said if white has already made inaccuracies in the opening then there is probably better ways to play for the advantage than trying to trade off a bad piece." White did not make any inaccuracies. The first inaccuracy is black's ...a5. To trade it off directly ...Ba6 works. ...Qc7 is probably stronger. The position is in balance, neither black nor white has any advantage. Black has a better pawn structure, but has trouble developing his King's side.

Where and how exactly Nimzovich recommended it? Do you want to say that the majority of masters just choose 5. Bd3 for no reason instead of recapturing the pawn, which is rather natural?
>> That is probably because your opponents misplayed it.
Okay, you can almost always say that. Obviously if Stockfish says -0.2 then my opponents should misplay it for me to win, because I can't outplay Stockfish itself with such an eval. I just say my opinion that it is hard to play for white for a human. If Nimzovitch could do this, I'm ok with it, but probably he had some ideas in mind which you didn't mention.

If I was White, I would have brought about this attack a little bit differently. I would have played 14.exf6. There is no need to worry about 14...Qxf6. Black has too many weaknesses for that major piece swing to be any concern. If he opens up as many lines as possible, I don't really see what Black can do. There is too much pressure.

#12 Nimzovich was the first to advocate and play 1 e4 e6 2 d4 d5 3 e5!. He played many games with 3...c5 4 c3. Then he shifted to either 4 Nf3 cxd4 5 Bd3 or 4 Nf3 cxd4 5 Qxd4 Nc6 6 Qf4. In Vilnius 1912 against von Freymann he played (misplayed would you say) 5 Nxd4 Nc6 6 Nxc6 bxc6 7 Bd3 just like this game. Later Nimzovich shifted to 4 Qg4?!.

#13 You are right. 14 exf6 was winning for white.

1. Instead of a5 you should have played Qb6 to put pressure immediately on him by targetting b2

2. Once you have captured on c6 with a pawn, you do not have a bad bishop anymore because you have a mobile pawn phalanx in the center. Q So you do not have to get rid of it anymore.