LS03

Hi,
I'm a female so I'm not too up on mechanics.

My IS200 starts off fine without trouble. Within 20 minutes or so of driving the car suddenly fire on five cylinders. The engine management light comes on.

If I leave the car off for about an hour to two hours or so it will drive fine again. Then after 20 mins it will start misfiring again.
So it seems something heats up, and that's casuing the problem.
This has gotten worse over a couple of months. It used to happen less. Now it's everytime I go out.

Codes are PO171 and PO303.
An odd time I get the code PO300 but not generally.

When it's misfiring, I hear gurgling noises especially when I start the car and it's still in misfiring mode and I move off from stationary. It gurgles intermittently while it's misfiring.

I changed all the plugs, and the coil on the third cylinder. Nothing changed with the problem except it ran a bit smoother.

Thanks for any help. Appreciated!