Yeah, you more than shorted a transistor, I think you probably blew your switch matrix. If it's returning more than one switch at once, you either have a physical short (unlikely, given the double activation with the flipper button), or you blew a chip that manages the switch signals on the mpu (probably u20). The coils are firing randomly in switch mode because they think the switch they're tied to is active. If you tell us exactly what switches it says are active when you hit another switch, we can probably tell you what failed.

Oh, no idea to be honest. Never even seen a PROC board. It wouldn't be the power driver though. You probably did blow something, but without schematics, I have no clue what.

How would he be getting any switches without 12v? I don't know PROC, but assuming it uses a standard switch matrix voltage, you either have switches or you don't. Optos might be an exception, but I don't think BOP has any, does it?