The fuel pressure regulator is bad, one or more fuel injectors is leaking or the check valve in the fuel pump is faulty.
NO.
A bad fuel pressure regulator will cause the car to stall or not run .
many different factors can result in a bad idle on a vehicle. some of them is the fuel pressure regulator, the throttle positioning sensor (located on the throttlebody) and faulty plugs & wires, or fuel injectors
I would try replacing the fuel pressure regulator. That was my problem.
A damaged fuel pressure regulator can cause a car not to start.
If this vehicle does not have an electric fuel pump, then the fuel pump diaphragm has a hole in it. Replace the fuel pump. If it is fuel injected, which I think it is, then you have one or more fuel injectors that are bleeding off after shutdown. Have the fuel pressure regulator and the injectors checked.
Could be a faulty check valve in the fuel pump, a leaky fuel injector poppet or a leaky fuel pressure regulator. My guess would be the fuel pressure regulator.
May be a bad fuel pressure regulator.
The gas is probably not leaking into the filter but the engine. It's caused by a broken diaphragm on the fuel pressure regulator. Replace regulator
Start with the obvious parts. Have the fuel pressure checked. Check the fuel pressure regulator, the fuel pump, and the injectors. If that's all fine, perhaps it's one of the sensors that controls the fuel/air mixture.
That would one of hundreds of possible causes.