Stop lights stay on even when the car engine is off

TURN KEY ON , REMOVE FUSES ONE AT A TIME ,TILL PROBLEM STOPS ,CHECK COMPODENTS , DIS CONNECT WIRES ONE AT TIME TIL PROBLEM STOPS,REPLACE DEFECTIVE PART OR RELAY

if your talking about the rear brake lights then you probably have a stuck or bad brake light switch, as the switch is always powered up even with the key off on one wire and only supplies power to the 2nd wire on the switch to the lights.

If your check engine light is on you usually have a code. Where I live several auto part stores will read the code for free. It would help to have a code.
If you have 2 fans on the radiator one should come on when you turn the A/C on. The other fan come on when engine reaches engine operating temperature. You have relay for compressor and the fan motor. Does the inside fan stop blowing. If a fuse was blown they should not work at all but a relay could drop out and in. I have found a bad relay over the years by checking the temperature of the relays, it is not always the case.. I have had a couple relays which were a lot hotter than the others, helped identify the bad relay. you can get the relay checked at the auto parts store. The low pressure switch could be creating problems with low Freon pressure. some info fuse relay below.
http://www.autogenius.info/chevrolet-cobalt-2005-2010-fuse-box-diagram/

Take to AutoZone for free check

look around the car on each door, you will see a small black switch on wich the door shuts on. This switch when open brings on the light and bell. Go around and check by pushing each one of these in. This should stop the light/charm. It works on what is called an open circuit, if you check each of the sensors and the problem persists, then one of the sensors may be faulty or their is a broken wire somewhere in the circuit. These switches should easily unscrew from the door frame. For the mean time to stop your battery going flat, remove the interior light globe.

the problem is like the alternator warning light came on because of lack of charging, but you says it is a engine light. are you sure?

this car has a light control module under the drivers dash to the right side of the steering colum. check there the module may be bad.

with the key in the on position, locate the reset button in the drivers side fuse panel,pess the button when the oil light blinks press again, should stop blinking and the chimes will stop, hope this helps

the plastic round stopper most probably broke that is were the stoplight switch sits when not depressed easy fix find a washer small enough to block the hole were the original plastic stopper was making sure the washer aligns to the brake light switch and secure washer w/ zipties hope this helps.

sounds like a swedish impòrt where the lights stay on all the time.