Finalize the sale of the car I listed.
The buyer will be paying cash when they receive their check this coming Friday
from their insurance company. How do I proceed to from here? Should I pay
off the rest of my loan?
The buyer would be a fool to buy your car if it has a loan on it unless they know the loan will be paid off in Full. You still owe the money even if you don't have the car anymore!
Also have a look at this link: https://cargurus.helpscoutdocs.com/category/273-p2p-transactions