/// Get it on a lift and look. There is nothing on the passenger rear that would cause that unless the owner installed something. The Catalytic converter is under the passenger front. Too much unburned gas will make that white hot. Is it undercoated? The white hot converter will cause the undercoating to burn. If the converter shield is coated it will catch fire. BTDT (Been There Done That) If the rear main is gone oil will drip down to the exhaust brace and when the exhaust system heats up that oil will burn. A leaking pan on the transmission will do the same but have a different smell.

You are on the money with the parking brake. Again get it on a lift. You should be able to see the cable move in and out slightly when the brake lever is pulled. It may be possible (with the lever off--down) to pull the cable with your hand (From under the car) and watch cable movement in and out of the shield. If you cannot get movement relative to the shield it is rusted, frozen.

Remind the seller that the car is worth no more than book value adjusted for over average milage. Every dollar he puts in is a dollar lost. NADA only goes back 5 years but libraries keep old copies that can be projected forward. Ninty four NADA would be the last listing.

If the covering on the hand brake cable has worn off the cable will get wet and rust locking on the rear parking brake, check where the cables emerge from the center of the underbody and run along the rear axel and enter the brake backing plate. The internal brake shoes inside the rear rotors are expensive.

The smell could be Trans fluid dripping onto the exhaust.

"had it for a couple of months and wife dosen't like it"

translation: found out repair costs were beginning to cause relationship stress.

$3400 is high for an 11 year old "second owner" car.