Hello and thank you for choosing Just Answer.
Doyou have problems when driving, under acceleration?
That is no a fuel pump nor fuel pressure problem. That is a vacuum/air problem that you are having. If you were having fuel pump problems the major thing that you would notice is acceleration and power loss.
You are experiencing problems with the Idle Air Control Valve. When the gas is not pushed (at idle) the throttle body is closed. The Idle Air Control Valve (IACV) is supposed to open up and allow air to bypass the throttle plate to keep the car running and at steady RPM's. If the car is shutting of or not idling smoothly you most likely have a dirty/clogged/bad IACV.
Here are the Removal and Installation procedure. You may want to try cleaning it first, if that does not help replace it.
The IAC motor is located on the rear of the throttle body secured by two Torx® screws.
Disconnect the negative battery cable.
Remove the air cleaner assembly.
Unplug the IAC motor connector.
Remove the two mounting Torx® screws.
Remove the IAC motor from the throttle body.
When the IAC motor is removed from the throttle body, do NOT extend the pintle more than 0.250 inch (6.35mm). If the pintle is extended more than this amount, it may separate from the IAC motor and the motor will have to be replaced.
Install the IAC motor in the throttle body.
Tighten the mounting bolts to 60 inch lbs. (7 Nm).
Plug the IAC electrical connector in.
Install the air cleaner assembly.
Connect the negative battery cable.
IAC motor mounting screws (arrows)