Immediate reuse means significantly less than 24 hours. Falcon 9's current cadence is fast enough to meet their current launch demand and doesn't need to improve, especially with Starship on the horizon. On the other hand, Starship will need to launch repeatedly in a short amount of time for orbital refueling to work.
So it was declared as a target, was possible but wasn't done because no demand? Knowing SpaceX they'd do it just for bragging.
The fact that it's required for Artemis to work, and the amount (nobody knows exactly but lower bound is like 15) of Starships required to launch in quick succession just highlights how risky, to the point of unsoundness, the project is.
They don’t need rapid reuse for Artemis. It would certainly help but Starship can just hang out in orbit for a few weeks while they do what they need to do to launch all their rockets.
It really depends - you can do direct injection to GEO now with cryogenic stages. And IIRC Soviets did some tests with kerolox stage (that should eventually launch on the ill fated N1) around the Moon, meaning multi-day flight times with liquid oxygen on board.
If you do the thermal design right, possibly use a sun shade (space is a large thermos bottle after all) or even use active cooling to remove the little heat that gets through, then it should work just fine. :)
The heat shield probably provides some degree of insulation from the solar radiation as well, and it's only needed on one side if you're far from Earth.
