yes a car adapter comes with a cigarette lighter 12v plug for easy use in a car. It's reccomend you cut that plug off and hardwire it into the car instead. It basically has a built in dc-dc conveter/regulator built in.
To have it turn on when the car is on takes some work. You wouldnt want to connect it directly to the battery or it would drain the battery when the car wasen't on.
Best bet it to setup a relay that's trigger when the car is on.