As long as you have enough credit available yes. Just remember even if the payment is from another source, you are responsible and it eats into your available credit until it is gone.
The difference is that one is for your vehicle (car) and the other is for your home. For both you are being loaned money and will need to pay them back but basically that's the difference.
Auto finance companies are very leary to lend to people that owe the government, so the answer is most likely no.Yes of cours you can get car loan if a student loan is in default there are many...