First, welcome to the board.
Second, please read the stickies in this forum, espcially the one about Descriptive titles. Your first two topics are covered in the Newbie FAQ thread (short answers here: 1 Run straight into the amplifier from the soundcard and 2 Don't see why not...but you'd still need an invertor)
3. It matters. VGA cable.
4. If he either shuts down the pc manually or has a shutdown controller, then sure--mine does...hibernate doesn't draw any power. If he just shuts the car off he's SOL.