They may need compiled to a specific architecture, but the actual driver code itself is pretty device-independent. Unless you're doing something like implementing your own bus instead of using something like PCI, aside from weird corner cases, the code at that level doesn't care.

Not when they are open source...

I never wrote a single driver, but I believe all bets are off with hardware. Drivers can execute logic on the cpu and on the chip, it's probably wild.