If by hesitate you mean it continues to run for a few seconds and doesn't turn off instantly, it may be a condition called "dieseling." It's a condition where the residual fuel continues to combust because the compression is still there. Try switching to a higher octane fuel, and it may go away.
no
Possible vacuum leak
I guess that after 15 min of turning the engine all the light go off, to preserve the car battery, but I am not sure
its not turning off and on its just losing and gaining rpm`s
check dimmer switch for headlights
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.
try turning the switch off
Loose ground
What is your car's year? Automatic or Manual Did the problem begin after working on the vehicle?
wipers don't shut off and the sunroof opens after turning off car, it a 2002 Lincoln ls
This is being caused by some fluid on the engine. You could have an oil leak somewhere and that is what is causing it to smoke only when the car gets turned off.
well for one is your keyed turned all the way off. But i would say you probably have a short in you wiring somewhere. But try turning off the heater while the car is running then shut your car off.