Call it a 'Queen's Pawn Opening'.

'Mutual Queen's Pawn (Opening)'

I think it is called losing a pawn. Not the best idea.

Blackmar Gambit, or Blackmar-Diemer Gambit if White follows up with 2... dxe4 3. Nc3.

'Blackmar-Diemer' - one of the more scary names for an opening - especially when spoken aloud. Black does best to accept, but life can be precarious for a while, at least.

Accepting the pawn is the most natural move, but 2... c6 simply transposes into the Caro-Kann, so it must be sound.

A very good line of the Caro Kann. Also good are 3.e5 (Advance varioation) and 3.exd5 - (Exchange Variation, which can lead into 3...cxd5 4.c4 - the Panov-Botvinnik Attack - one of my favourites).

This isn't so good; the bishop is blocking the pawn that lets out the other bishop. Better is 3... dxe4, even though it no longer wins a pawn.

Taking with the bishop may have been slightly better.

White has rather badly weakened himself on the light squares.

Right idea, but slightly more accurate is 9...Bf5, first, and then 10...Nb4 if White doesn't play 10.a3 to stop it. This way, ...a3 will cost Black a little bit of time, though the knight's regrouping to c6 will not be unwelcome.

That really is a dreadful move, no question about it. It will lose more than the knight, if black exploits it properly.

Yes. Black has a well developed position and now has the advantage of an extra Knight.

All recaptures were strong. Best was in fact 10...Qxd5, attacking the rook, but 10...Nfxd5 and 10...Bxd5 were also winning easily. After the text, Black is winning also, but the task is slightly more difficult (less easy).

I would have played ...Bxd5, Rg1 Qa5!! and black is without a doubt winning.