a little WD 40 should do the trick
I would try either a strap wrench, or, a pair of vice grips with a thick cloth covering the nut.
a welder and a cutting torch. or you could just tear them off completely and use netting which would look cooler!
check your shifter bushings, next would be inside the trans at the shift collar.
They get stuck because of overactive use and dust/mold buildup. I would use an aerosol can and try to remove the filth.
The best tool - would be a pair of small tweezers. That would probably help you remove the piece stuck in the socket.
I would use a chemical stripper.
The air doors maybe stuck. Or selector switch is not is not operating correctly.
Transmission, yes Motor no, but it would be easier if it was out.
Our both doors have become stuck on our kia carnival 2001 model and it is the rollers they slide on dont know why thay have done it but they cost about $150 each to fiix.
FREAK
No, it will not.
food stuck between your teeth would stay there for longer because there wouldn't be liquid to help remove it.