Hey there and welcome / welcome back?
I'll keep the answers short for now on the questions and then give my own thoughts.
1: If i am not mistaken, the xbox360 is a 12v device?? instructables.com MOD - Picture of PSU in there, 5v also (you can step down the cars voltage easily with various methods).. This would be the best option and fairly cheap to do... free if you have the parts already around... also try not to run the inverter of the accessory socket
2: When it comes to cables and running them in a vehicle, try to keep power cables to one side and signal/video/audio to the other side.. The car "may" already do this with the stock stereo. Otherwise it should be fairly easy to remove the center console and run the cables under there and the carpet (depends on the car)
3: The length of 1 meter seems to be the recommended limit and possible to 1.5m if you are lucky for a SATA cable. (eSata maxes out a 2 meters)
You'll need to most likely have the xbox/board within a proximity of the drive including cable running.... maybe time to lose the xbox case or relocate it?
Thats the main things that come to mind at the moment, also from what i recall you can not use a USB drive either on the xbox (dvd/cd)...
- Networked: never done it but how about networking the xbox so you do not need the drive, depending on what your doing... not sure how limiting this is ?
- USB Key/HDD: Is it possible to operate everything you need with a USB plug instead?? songs and videos on a USB hard drive / key??
- Another System: many reasons, for example i'm about to try a Raspberry Pi .. very cheap and will cover what i need easily... If the xbox is just for games, then ignore this one.