hi AMW.
Sharp loud noise can be related to starter gear disengaging from the flywheel when the solenoid retracts. The result can be one big clunk/knock. It's not necessarily a problem, if that's what it is.
The whining noise could be the alternator charging the battery.
I'm not aware of there being any air compressors in the car aside from the 8 pistons...
regards,
/e