Why does it cut off while driving, but starts right back up?

be checking emissions controls for vacuum leaks especially with the brakes..

Are you shure that it isnot overheating?

The warning lights on the dash will come on when the engine dies.
If it dies and starts up like you turned the key it could be a relay or other electrical problem. May be tough to find if you can't test components while it is not starting.
I assume the check engine light is not on when the engine is running.

replace the air and, fuel filters

giv it a tuneup-change plug wires and distributer cap etc--fuel pump or regulator may be failin--go down to a discount place and git car scanned

sounds like the auto choke isnt turning itself off properly but to be totally honest i would need this to happen when i test drive it to diagnose it correctly .

It sounds like you have a bad MAF (Mass Airflow Sensor). This is in your air inlet tube, pull this out and check to see if there is any corrosion on it. If is one that has a coiled exposed wire, then ensure that the wire is not broke.

plug wires for sure are bad with it backfiring

its going to be the saftey neutral switch please respond

This was the fuel pump. Checked the fuel rail and no gas. Shook the car and it started, but shut off after a moment.