Do apples have a bios?
No, not in the traditional sense you're thinking of anyways. Someday PC's won't have one either. A bios is considered a clunky way of handling hardware functions and the computer industry wants it gone eventually.
You can access certain hardware functions though. See: Open Firmware
I use to work for an authorized Apple repair shop but that was back in 1992. I wouldn't attempt messing with system settings now until I was absolutely
sure of what I was doing. Probably childs play for a mac enthusiast though.
The symptoms do sound hardware related. I'd be looking for a pattern here. Does it always reboot using a specific program, does it do it only after it's been on for a certain amount of time, etc.
One things for sure, if it was mine and a new system, Apple would either be replacing it, fixing it or wearing it.