Do I sell my 2007 Kia Sportage or Pay for the Repairs on it?

Absolutely agree. That is not going to happen. If I come to buy your car and I see the rust, and the bald tires, and find the bad bearings on a test drive, etc etc, I’m going to know that I have to replace those when I buy it, and I will reduce the price of the car from blue book appropriately.

So, you aren’t going to get bluebook value because it’s not worth anywhere near that much. Your car’s worth a little under 2 grand in fair condition (and it’s actually worse than fair if the rust is as bad as you say). The cost of repairs is probably around the value of the car, which means prospective buyers are going to want it for basically a few hundred. $500 if you’re lucky. You will still have to pay off the loan after you sell it, so financially I think it makes more sense to carry out the repairs and keep the car.

If you’re taking it to a dealership, don’t. Take it to a local independent. They’ll probably be cheaper.

I would ignore the rear quarter panels. The “it’s close to the fuel tank” statement is dumb because it’s not. The fuel tank is attached under the car, not to the sheet metal of the quarter panels. Most likely, the rust is ugly but not a safety concern - but you should show us a pic to be sure. Not fixing the rust will take a big chunk off of your repair bill. You can probably do the rest for around 1500. Even less if you find a used tire shop.