1 - You need someting like the Fusion BRain to control the motors. It can be done, but you're going to have to do some creative engineering.
2 - You want physical buttons for volume control? The PC has its own volume control and front-end software makes it very easy to adjust volume with a flick of your finger.
3 - Wire a switch to the ignition-switched line that runs to the DC-DC PSU. It will cut power to the ignition line and the SDC will shut off/startup the PC. In addition,if the switch is off and the car is started, the PC won't power on.
4 - That's up to you, really. You need to determine where you want to mount it, and how much fabrication you're willing to do (or pay do have done) to make it look the way you want.
5 - Don't expect the PC to go into the dash unless you lay hands on PIcoITX hardware (pricey). A miniITX motherboard will barely fit, and the cables connected to the back will make it too deep for most dashes.