Right, firstly, your sound and screen "waves" are due to improper grounding, and/or running the PC/screen on unregulated power. Once you get your power sorted, and hook up the power of the screen to a regulated supply, it will be better.
Most of your problems are power related. The power supply can't take the voltage drop when you start the car, hence why it is crashing. You have a ground loop somewhere in your audio/computer setup which is causing the "whining" you get in relation to engine speed.
As for touchscreen issues, the Lilliput is fussy, but again it could be due to not having decent power.
Aux input i'm afraid I can't help you with, as I don't know exactly how you've done it, that's something you'll have to sort out for yourself