Well I would not be comfortable with DC to AC convertors or invertors. Most of them are not long lasting. Instead you should buy a laptop car charger specific to your model. It would not put much strain on the car electricals as compared to an invertor. Remember to use invertors when the car engine is running otherwise you will lose yoru battery charge rapidly.
Secondly yes it is possible to listen to music from your laptop to car stereo system provided you have a specific cable. Check with your audio shop electrician.