should the baby biob filter be on 24/7?

Answer 1

Yes, yes it should. If you turn the filter off, the ammonia and nitrite detoxifying bacteria on the filter sponge (or the weird gravel/stones at the bottom of the tank in the case of the biorb) will not be getting enough ammonia because the water isn't circulating around them, resulting in them dying back and an ammonia build up will happen - harming and possibly killing the tanks inhabitants.

If only they could make those filters silent, eh? : ).

Answer 2

The bacteria that keep your tank alive start to die at about two hours without aeration. Keep it running.

Answer 3

Yes.