What I did with my lcd was to buy a fuse tap and tap a fuse that only had power when the car was on. I ran the new power line to the lcd. The fuse tap was rated like 10 amps, but lcds usually draw only 1 amp.
For the laptop, maybe there is a setting in your power options to shut the laptop down when the AC adapter is unplugged. Cigarette lighters are usually switched with the accessory ignition switch.