yes it does... the power to the drive has no effect on the firewire signal... however there is no power button on the device...so it will stay on unless you turn of the power to the adapter or unplug the power cable... the rest of the time it automatically sleeps depending on inactivity :)
I wish I could say I knew but I don't. That might be a good question to ask the company directly... I leave the MacBook plugged in as the default and working as our backup drive so I leave both on to backup in the background. Sorry I can't help more than that.