To power the LCD you could do one of 2 things. Some LCDs have a DC input and use a power brick. You could figure out what the voltage is and design a regulator to regulate your car's power to that of the LCD. If that's too hard you could get a power inverter and use it to power the laptop.
I don't think vibration would be much of a problem for the laptop. It's built for it.
The Audio out depends on what type of car you have, or what type of radio you have in the car. If you have a head unit with Audio in, then it's very easy. Otherwise you'd probably have to go with an FM Modulator or Tape adapter.