When oil is warm and the car is idled the oil pressure will be lower than when cold. If it's too low it'll shut off the power to the fuel pump. Also the Fuel pump relay can have the same effect. If the oil pressure switch is bad it'll turn off the fuel pump at a higher pressure than it should.
There's more variables that need to be answered to help us help you.
When you say backfires do you mean Backfire through the intake or Popping the exhaust.
These are two very different effects for different problems.
Through the intake... Ignition is advancing too far. (module, TPS, Temp Sens)
Through the exhaust Retarding ignition, too much fuel, complete misfire. (Module, Stuck FPR or line off, Map, TPS, Temp)
Stumbling bad spot on TPS, Module loose, Arcing in Coil, bad Coil ground, Map, Vac leak, Low/intermittent fuel pressure, IAC)
Anytime you have a stumble and an exhaust pop it's due to the ignition retarding so far to try to recover it ends up burning fuel into the exhaust. This creates the pop. If the fuel pressure drops then the stumble will happen, Fuel pulses will get longer to add fuel, ignition will retard, IAC will open, and when the fuel comes back on you dump fuel in, have extra air, and a late spark and then the burn finishes after the exhaust valve opens.
If the ignition is shutting off then you get fuel in the exhaust combined with the rest of the above resulting in a larger combustion in the exhaust.
Lots of variables.
Find the testing procedures for each and every sensor. Take time to learn them. it really helps when you can run a sensor check. Get an analog and a digital meter. Learn them both. Analog meter is about the best way to see an intermittent problem in a sensor sweep.
Maybe one day I'll set up a decent Sensor test kit to add to a Community tool program. Complete with sensor emulators.
Stu
[This message has been edited by DIY_Stu (edited 03-12-2011).]