My cobalt's engine is surging from 500 to 800 rpms when I come to a stop What's the problem?

You have two problems. The surging is from a dirty throttle body and /or air filter. The selector light could be from a bad selector switch or internal transmission problems. Have the car scanned for codes.

Clean the mass air flow sensor and inspect the hose from the throttle body to air filter box for cracks or air leaks

Take it to a shop. Don't fool with it. It has to do with the traction control.

first check the throttle plate for carbon build up the look for the knock sensor harness rubbing onto the fan shroud

Has it done this since new? The computer has a built in Rev limiter, its job is to prevent damaging the engine from high RPMs.

Btw, I’m available to help over the phone in case u need at https://www.6ya.com/expert/mike_a0891ab86974ea74

i have an 06 cobalt with the same issue and when my engine light finally came on it showed up as evap system malfunctioning. This is for the emissions system. My code shown was P0440. This can be caused by a faulty or loose gas cap, a purge valve, a vent valve, or the evap canister. I am waiting on the purge valve to arrive now so should know if that takes car of mine in a week, but i have already replaced my gas cap and the problem is still there. Hope this helps you some

replace the idle speed control motor

block off vacuum hose to brake booster and see if idle returns to normal if it does you need new brake booster has hole in diaphram internally some times slight hissing noise is evident in cab when pressing brake pedal to section where engine surges or idles high. also check for fuel leaks from hoses if you can smell fuel in engine bay while running and engine warm some leaks only leak while running and hot

Easy fix... Take a gallon of gas and a clean cloth or shirt. Soak the cloth in the gas and wipe all the interior down with the gas.

Then poor some of the gas all over the engine, making sure to soak it really good

After doing this, take a match and burn that f**ker..
Mine was doing the same thing, I burned it and blamed it on Islamic jihad to my insurance. Never looked back

it is probably out of water as mine did that and the radiator was dry. due to a bad water pump.