Started before when jumping it, but now just turns over.

While on the freeway, my 2001 X5 (165,000m) car developed a coolant leak, overheated, and was towed to the dealership. I was told there is white melted gunk in the radiator, so the radiator needs to be replaced. And I was told that we won't know if the engine damage is catastrophic until after I have spent the $$ replacing the radiator. Should I repair the radiator and hope for the best, or is it likely that my engine has catastrophic damage?

temperature gauge rises to show red, then settles to middle when driving, goes red when at stop. Same route may have no change in gauge the same day under similar conditions

Changed water pump, car does not overheat but upper radiator
Hose disconnects from expansion tank under normal operating temp

"service engine soon" light is on. OBD2 code P0412. No drivability or engine performance issues.

no sound of d fan what should I look for to get heat

I arrived at my location and a/c remained on when I turned car off.