A normal day light would be better, at least thats what I think.(I also haven't owned a bp for that long) But i do have one heat lamp and i leave the lights on the day time, and turn them off at night.
He should be fine eating. My first one(rescued) ate the first day i got her, although she was starving. If he doesn't eat the first time, probably wait a day or two to try again. If he eats live only DO NOT leave them unattended for even a second.