1: Well you can always buy 8-9-10" screens but if it will fit in nice...
2: For your plan you will need a inverter for like 300 watt. You setup isnt excactly lowpower with the cards.
3: Check out the software section
4: If you have a normal case then yes, maybe there is some room under the backseats or else on the spot where the spare wheel is? Thats why most people have VIA boards, theyr small! I put mines behind a panel in the back of the car
5: It doesnt get that hot, you can back clock your pc a bit or install some fans.