Antediluvian

removing the GPU is a good choice
i would also suggest removing your CPU cooler if it's a big tower heatsink, AIO are fine if you used all the screws to keep the radiator in place, stock coolers are also fine
 
as for hard disk, dont worry too much about it unless you're going on gravel road
put a cushion under your PC and make sure it doesnt slip/flip and bang around in the car and you should be good
 
also, having a backup isnt a bad idea anyways

Coil whine is a very normal thing. If it's absolutely horrid, try and RMA. Most companies won't though.

If it's a GND pin it should be fine. If it's just about any other pin your computer probably won't POST without it.
 
How bent is it? If it's not terribly you can usually bend it back.

You can try bending it back careful. Worse case scenario you could try following the second half of this very old Linus video:
 

See how you perform. If not, pray and grab some tweezers.