Magic Mouse

Magic Mice are not Bluetooth multi-homed, so even though you can pair the same mouse with two Macs, those Macs need to be out of Bluetooth range of one another, or the first paired takes control of the mouse.

If the two Macs are close together you can tell one to forget that mouse and then pair the mouse to the other Mac.

Yes also if only one Mac is on at a time.

Yes.

Viking is correct. I should have mentioned the Macs can't be in close proximity.

Just to add, if only one Mac at a time is booted, there won't be a problem.