There are two main lineages of head lice that split up right around when humans left Africa. Theory I heard is that one probably came from Neanderthals and went back to humans as the two groups...met up.
Probably. There's a type of fly in NZ that is wingless and rides on bats.
Most of the flies live in bat nests but pregnant females cling to bat fur and go everywhere with them, which makes sure the species is never left behind if the bats move nests.