No one has mentioned a hardware fault!
With my previous N900; the bluetooth would only work when you first connected, on the second attempt, BANG the phone would crash so badly that I would have to take the battery out to restart it. So strange behaviours can indicate odd little hardware faults where you might not expect the hardware.
Also try switching Wifi when connected to different routers (different makes) also try when not connected to Wifi
I would also do as kinggo recommends, a reflash, if after that it still reboots then it's hardware and Nokia needs to have a look.