When engine starts, idle races aat varying speeds.

What is to high? 2000RPM, 2500RPM? Also cold idle and start up idle and many other factors vary with make, model and type of engine, smaller engines in most cases need a high start up idle.

This is usually a problem caused by a bad water temperature sensor. There are usually 2 sensors with one working the temperature gauge and the second working engine controls.

The "cold start" sequence is similar to a choke in old cars. It needs the signal from the water sensor to trigger the cold start sequence. The cold start sequence enriches the fuel charge, adjusts timing, and increases idle speed until the engine gets a little warm.

Now if stalling when warm, you have other issues. Manifold runners are a problem on some engines.

Should be on or near the fuel injector supply rail.

Low pressure from fuel pump, when the pump is cold the pressure increases, as it warms up the pressure drops (this happens in a pump that is going out) the normal pressure should be at 40 with the key on and engine not running, when started the pressure should stay around 36, any less it won't idle and may run as long as you hold the pedal down. The injectors are opened electronicaly, so as long as there is fuel flow the engine gets fuel to run.So check the fuel pump, soundslike you need a new one

Could becaused by a few different thing's . Map sensor , idle air control valve , a vacuum leak . Having the vehicle's scan data viewed would probably pin point the problem . Do you know what scan data is ? Is what a professional tech uses to find problems .
084 Engine Mechanical Tests Scan Data for Vacuum Leak
007 Idle Speed Problems Scan Data for Idle These kind of test's are what seperate week end DIY'ER's from a professional tech.

Engine stalls or RPM fluctuates at idle up and down or dies near idle.

This problem is commonly caused by a dirty automatic idle speed control valve and throttle valve but always run a OBD2 fault code as well as the cleaning procedure. Buy a can of throttle valve cleaner (do not use carburetor spray cleaner!) from NAPA or Carquest (made by CRC chemicals) and spray it into the air intake while the engine is running, use up about 1/2 the can, engine will try to stall hold the speed up, shut it down and let it soak for 30 minutes, restart and blow out the remaining fluid, shut it down and disconnect the negative battery cable for 5 Min's to reset the base idle control

Common issue on this year and engine, Do the cleaning outlined below.

Throttle Body Cleaning

You can in most cases repair this slow speed stall or unstable idle by cleaning the engine throttle valve and the idle speed control valve using a product called CRC Spray Throttle valve cleaner. Spray the cleaner into the air intake of the engine with the hose removed from the throttle body, the engine will try to stall so hold up the idle speed manually. Once you have used up about 1/2 can of the cleaner stall the engine out while spraying and turn the key off, disconnect the negative battery cable for 5 minutes and then reconnect and drive the car for a about 25 miles of varied driving modes. If this doesn't cure the problem you may need the fuel injectors professionally cleaned by the dealer service dept.

I would start with cleaning the throttle bore and plate. Then clean the Idle Air Control valve, IAC, as this is the device that controls idle speed. Use a can of spray carb cleaner and an old toothbrush. Trouble with the IAC would make sense if you can keep the engine going by holding down the gas pedal a bit.
Use the carb cleaner to check for vacuum leaks at hose connections and elbows. run engine and spray short bursts at hoses and listen for idle speed changes.
And lastly if problem is still there check MAP sensor.

idle speed is not adjustable on this engine, here is what i do for the probelm.

, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.

replace idle control sensor.