Car has 62k miles. After driving for a while, and stopping for around 30 minutes, the car, when restarted, goes into restricted performance mode and runs rough. In the past, all I had to do was rev the engine for a few moments, and the engine would smooth out and resume normal operation. It happened today and set the check engine light for the first time. I retrieved the following codes: p0300, p0301, p0302, p0306 and manufacturer specific code, p1316. I have suspected that it is a fuel problem, but would like y'alls opinion. I recently replaced the fuel pump, but the problem existed before it's failure. Thanks, in advance...!

 

I would start troubleshooting by swapping cylinder1 with cylinder 3 coilpack.
Cylinder 2 with cylinder 4 coilpack and then cylinder 6 with cylinder 7. Once you have swapped the coil packs clear the codes and drive to see if the codes reset to the new locations. If the codes travel then you need to replace the coil packs.
If they don't travel to new cylinders report back and we will go on from there.
Don't do a lot of driving until you get that code 1316 clear. It is excess emissions and can damage the catalytic convertor.

 

Maybe you have 'dribbly' fuel injectors??
They can leak/drip causing flooding in certain cylinders and also you lose fuel pressure.
The heat soak can cause vapor lock in unpressurized lines???

Just a guess.

bob