The big technological thing Tesla batteries have going for them is, short of complete mechanical destruction, they don't catch fire. There's a thermal shutoff on every cell. So not the big issue it might have been.

I doubt many homes would have adequate fire separation between a garage and main home to make a difference between laundry vs garage.

It may not make much of a difference from the overall perspective of damage, but it certainly makes a difference in warning and escape time. Also, the chance of dangerous fumes while trying to escape is lower.

Depends on design. Garage could share a wall with a bedroom and the laundry could be on other side of the house or vice versa. I would say that garage may be the most obvious choice, but not always.