My C6 hearing noises
#2
Burning Brakes
Fans run to dry off humidity off the ac. My Kenwood head unit has an internal fan also that powers down, and there are some other noises from the car's electronics that power down minutes after you shut the beast down. The most important thing is that the noises completely stop after say about 10 minutes.
#3
From the engine compartment? That's the engine cooling fan. When you turn off the car, the engine is still massively hot. The fan runs to keep things cool, especially considering that you are now sitting still with no passive air movement.