2001 Cadillac Deville head gasket

Those engines have been known to pull the threads out of the block causing the head gaskets to fail, that is probably the reason for the high cost.You can try to get them down on price, but you may not have any luck, it is a big, labor intensive job.Whether or not you fix it is up to you and your situation.

The dealer has decided to split the cost with me, so
I will do the repair, but, how are they/me going to know it's not the intake manifold gasket, a cracked
head or engine block.

I do not have coolant in my oil, no white smoke, never overheated, my engine got hot, once, I stopped right away.

What do you mean by the engine pulls the threads out of the block, can it happen again?

Any idea what usually goes next

The original threads were aluminum, a design flaw. The repair involves steel inserts, called timeserts, to be installed. I have not seen a repeat head gasket failure on a repaired engine in my career with Cadillac(12 years). The fact that they are going to split, on a 2001, is a good gesture. The intake manifold has no coolant passages in it, and besides, that would not give you combustion gases in the radiator, since it is pre-combustion chamber. Cracks in heads and blocks are relatively unheard of.