Correct.
Yes. Detonating mines happens prior to the decision on whether or not to stay and fight.
Blitzing is always a unit’s first move into an adjacent territory, and does not require supply. As for Tripoli, page 18 says: “Attacking a hostile territory that does not contain enemy combat units still requires an attack declaration, but as no actual combat will occur, you don’t spend any supply tokens (instead, take the attack arrow from the general supply pool).”
Thanks,
Matt