This is a great commentary, Thanks. I learned a lot, especially about the Caro-Kann.

The idea is to oppose the advance d4-d5 by moving c7-c6. As for the French defense, Black plays c7-c5 (attacking Al-Qaida 'd4'), its principal counter-attack weapon.

I am not a Caro-Kann expert, but this looks a bit premature.

Agreed CK typical structure is Bg7,e6

I usually play c3 as soon as possible, because I feel it is needed to fortify d4. But in this case it is irrelevant which comes first.

IMHO, this is not the most precise move, I would prefer c3 first. The thing is that c3 is almost obligatory due to pressure against d4, and after that sometimes Qa4 (Qb3) is a good tactical option. But it all depends on your plan, sometimes it is good to ram the a pawn all the way to a6 (then b7 becomes vulnerable).

well .. almost, but you lose a pawn with Bxf4 Nxf4 Qxd4 Ne2 and black has good play

12. Qd2, Be2; 13. Be2 looks OK. I don't like to play moves such as 12. f3, usually they turn out to be weaknesses in the future course of the game (even if they are tactically justified at the moment). The reason is that it can become difficult to look after several weak points and/or lines/diagonals.