Okay well first off welcome to the mac side of the house. It is always more fun when you go with Apple...and when i say fun i mean challenging. Okay lets get down to it shall we.
1. First off the touchscreen will not work with the Apple TV unless you hack the apple tv to turn it into a full working OSX machine, even then it might be tricky. The basic software that apple TV uses does not allow for mouse clicking. You will have to have a keyboard in your car which makes things quite awkward for driving.
2. You do not need a soldering iron at all to insall a mini in your car. You can do several things. a) you can buy an inverter and run everything off of that, however there is a good chance that you will get feed back and more background nosie. b) you can buy the mac pac with the 1900 to power the min and all you have to use too hook up the wires is some crimp clamps with some black electrical tape. I know this isnt the ideal situation (soldering obviously is) but it will work. I have had my system hooked up like this for 3 years and i have had no problems.
to syn your music it is going to take a god awful long time. You have quite a large collection and i would suggest syncing parts of it, just like playlists. Since there is no mini that has that kind of storage capacity i would suggest in getting an external hard drive that you can syn in the house instead of doing it over wifi.
if you have any more questions please feel free to ask.