It’s weird indeed that the transmission only acts up on left turns, but that symptom could be a transmission problem, possibly requiring a rebuild but maybe just replacing a solenoid or making some adjustment. I’d probably start by giving the transmission a proper service if such is due. After that, you’d need to take it to a transmission specialist for an opinion.
The gas odor problem is probably something simple. Picture how it works. Most modern day gas tank systems are sealed, but they have to allow air in otherwise the tank would collapse as the gas was used up. The top of the tank is filled with air and gas vapors. When you fill the tank, it drives the air and gas vapors upward. They are supposed to go into a tube and be directed to the charcoal canister. Then the canister is supposed to occasionally vent into the intake manifold, usually controlled by a purge valve. Something must be wrong w/all that. Check for DTC’s before making any assumptions. Hopefully the vehicle’s ECM already knows what the problem is. If pressed for a guess I’d say it was the purge valve is on the fritz.