I'll start with your line of play. After 9. ... d5, white's next move might be cxb7, followed by Bxb7.
At that point, my engine evaluates this as roughly equal.
The white king isn't in any more danger on e3 than he is on e2. My engine prefers 8. ... bxc6. I do, too. Keep the tension between the bishops. If he captures, then you've either undoubled your pawns or opened up the a file. I'd tend to prefer that. Doubled pawns on c will help your center, and opening up the a means your rook is in action without having to move it! So I would expect white to leave your bishop alone. That means he needs to either move his or constantly guard it.
You have a favorable position at this point.
I have won an exciting game today. For the first time i managed to try up what i think is called Vulcovich countergambit against the Ponzani opening. Of course the opponent quickly went off the line i have memorised forcing me to think for myself.
When I analysed the game with the engine, it turned out, that iI have found good moves, but only about fourth best ( depending on how long computer counts). The problem is, i don't understand why is engine proposing what he is proposing, the moves seem ilogical to me.