Something has to be really messed up for you to only be getting 12mpg... Does the car struggle to build RPM when you give it throttle?? Im thinking a clogged cat. could be killing your gas mileage, and if it's clogged bad enough, it could be causing the engine to die.
And for the engine dying, does it only happen if you turn the wheel?? I ask because I've driven some cars that the RPM's drop off when you turn the wheel past 1/4 turn or so, and if your car has some problems already, it would easily shut the engine off.
If you can, check the cat. and replace O2 sensors.
If you start the car, and let it sit at idle, does anything happen??