Some cars have a cooling fan to cool the engine and keep it from overheating. I had a car with this fan when I lived in southern CA. If you parked the car in the sun, at times it would start up, bu itself, an hour after you had turned the car off. Sometimes, they stay on after you turn the car off. Check your owner's manual. If you don't have one, go to the Library. They have all kinds of manuals.
Headlights run off the battery not the ignition...
Because it's in park.
The throttle may be jammed. If the car has been unused for a period of time make sure that the throttle mechanisms are well lubricated.
You have something that's draining the battery. Something that is still using current even though you have turned the engine off. Something like a GPS or radio or fan or ??? Something that is still running or wired directly to the battery. One way to find out which circuit it is - With the key turned off, pull all your fuses - one at a time - and see if you get a spark when you re-insert it. The circuit that still has current flowing will spark a little when you push it back into it's place. Check all fuses. I am assuming this is an older car and this trick won't screw up a computerized car.
Your car battery could be running low so what you could do is get jumpleeds and get an other and jumpwire it
Could be that your idle speed is too high, or engine is running too hot causing the PMC to deliver a richer mixture,
No. The power to illuminate the Daytime Running Lights (DRL's) is supplied by the alternator, and does not have to be supplied by the battery. Once a vehicle is started and the engine is running you could remove the battery from the car entirely and everything requiring current would still operate.
She still has to pay with the car working or not.
A malfunctioning the ignition switch will allow the car to keep running after the key is turned off. You can remove the positive ground cable from the battery to shut the car off.
Make sure that the switch on the top of the steering column in turned off. That controls the running lights on the car. FYI that switch is basically used if you are pulled over somewhere and don't need help but yet you need your lights on and still need to take your keys.
Its not your engine. Its the fan running to cool the engine down. They all do it and nothing is wrong with your car.
igination on car is turned off but car still runs