The full capacity of the 6.0L oil system is around 18 quarts. 3-4 quarts do not drain out in the oil change procedure.
The oil pressure switch activates at 5 psig. So, below 5 psig there is no oil pressure on the gauge. I am like cartmanea - I ASSUME the idiot light comes on then .... but I do not know for sure.
I do not know about the "minimum" oil level for the HPOP to function, but I assume that all is needed is for the LPOP to be able to get suction from the pan and flow the 20 gpm it is designed for. The pan holds about 14 quarts, and I would bet you would have to be VERY low for the pump to lose prime and/or be below the required suction pressure.
I'm not sure how much this helps, but I vaguely recall working on a truck that was on my doorstep for a massive external oil leak complaint. This particular truck needed about 5 litres of oil top-up just to bring the level back up to visible on the hash mark on the dipstick. The truck started and ran fine. This particular truck had a massive pressure leak that originated from the top of the high pressure oil pump, the moment the engine was started. I guess that explained why it was THAT low very quickly.