The polarity of a car cigarette lighter adapter

You can connect the grounds in one point or leave them separate. As long as the only common point between the two circuits is the isolated power supply you are free to do as you wish.

If OTOH you want to connect them somewhere (to use the car antenna or sth.) then you should carefully choose the connection point (or even points) to avoid ground loops and ground noise.

Ultrasonic sensors seem to be the sensors of choice for many car alarms. You can often buy electronics kits which use ultrasonic sensors to detect motion. The outputs are often simply in the form of a relay, so you can connect it to almost any other device you can think of. Google around for 'ultrasonic motion detector electronics kit'. There's a bunch to choose from.

Simply mount one of these inside the car, and wire it up to the 'deterrent' transducer on the outside.

Alternatively, you could simply wire it up to a wireless doorbell, and leave the chimer by your bed at night.

Also consider wiring it up to a couple of cheap little video cameras, so that you can grass up the little urchin to the police.