2000 grand am rough idle, sounds like it's missing once it's been running for a bit.

ok check your fuel filter and your air filter it sound like dirty fuel

do you have a check engine light on if so need to get it scanned they scan them for free at your local autopart store need code

pull the air intake hose off the throttle plate, you will find a lot of black carbor around the throttle plate causing idle concerns. clean this with a intake system cleaner. this will smooth out the 2.4 liter quite a bit

Dont start it up anymore till pull the front cover off and check the timing belt as it sounds like its stripped a tooth and jumped over and now its banged the valves but i am known to be wrong with my diagnostics but check it out anyway .

Hi
Pop into to your local garage and have a diagnostic test carried out.
Listen to the advise given. It may save you lots of money, especially if you start the "guessing" game.
It does sound like a part may be blocked or failed though, but the sytem needs to be tested thoroughly first.
Good luck
Roger

Need more info... What kind of noise and when do you hear it?

If you haven't changed the plugs\wires, it may be time to do so.

usually rough Idle is not noticable at high ildle. Once it is idles normally try Disconnecting one injector at a time. If the idle stays the same than that cylinder is the culprit. Remove that spark. If it is wet than do a compression test. Should read better than 100lbs of compression.If compression is good take a spark plug and hook it into the end of the plug wire.Lay it across the intake,start the car and watch for spark. If you have spark than you probably have a bad injector. A miss will cause the vehicle to idle high. The computer is trying to keep the car from dieing out. Hope this helps. No spark do a tune up.

i would first change the fuel filter with it being run low in fuel it may have picked up some trash off the bottom of the tank so change the fuel filter and see if it runs better

run a fuel pressure test, if that checks out fine it may be a faulty coil pack or ignition control module

What size engine 2.4 or 3.4 L ? Dirty throttle plate , fuel injector's need cleaning , EGR valve sticking open a little , intake manifold leaking , IAC - idle air control valve passage carboned up .
Idle Air Control Valve
007 Idle Speed Problems Scan Data for Idle