Revising this message for simplicity:

Instead of my long story about Marvel Mystery oil, I now think that was a coincidence. Here is the short story:

My car seems to have a fuel delivery issue.
It doesn't seem to be bad gas, fuel filter, or fouled injectors.

All I know is that the fuel pump is good, good pressure at the rail, and if you remove the fuel relay and jump it the car works reliably.

I originally jumped the relay to confirm the fuel pump was working fine, and bought an extra relay in case I found out the relay wasn't working, to save a trip to the auto parts store. When it ran better without the relay, I put in the new relay for good measure. It drove fine for a while, but the problem of no starting/driving is back!

This 99 has something that looks like a pressure regulator by the fuel pump on another line. Sometimes it makes a soft rush after the car turns off. Is this normal or could this be a fuel pressure issue?

Scratching head....

 

could be the fuel pump or check into the EVAP system components - it has a vent valve and a purge valve which can stick. I believe your model has a fuel "loop" ie fuel goes from the pump to the rail and then feeds back into the tank (which is why a loose gas cap can throw an engine code. Try measuring your fuel pressure at the rail - there's a schrader valve you an measure from. Also you may want to check the fuel pump relay -but given you are getting a code for the pump, I'd be suspecting that's the cause. If you do the pump, its a good time to do the filter...

 

When I pulled the codes for the car, I replaced the 02 sensor and all codes went away.

I just made a list of parts in the fuel system that apply to this car:

fuel filter - already changed
fuel pressure regulator
fuel pressure regulator dampener
idle control valves
idle control hoses, inlet and outlet
throttle position sensor
camshaft sensor

mass air sensor cleaned and new air filter.
new 02 sensor as well.

...anything jump out at anyone?