That touch screen is only the overlay for a EEEpc, so it won't work very well. you might be able to use this or something similar with a 7" vga non-touch screen, but that is alot of work for not much cost savings.
look here for touch screens: http://store.mp3car.com/Monitors_and...reens_s/21.htm
you might also be able to find one for cheap on ebay, just make sure that it has a vga input, and has a touch screen that will connect to the laptop(in case doesn't have a serial port) most are either serial or usb.
I can't be positive(someone else might know better), but it looks like that is a double din opening for the radio.
if it is, there are a couple of sources for DD dash kits that would allow you to install a 7" monitor without cutting up your dash, and give it more of a oem look.
both mp3car, and bybyte.com have good ones, I have been using the bybyte frame, with a 7" lilliput I got from mp3car.
under the seat is really dependant on how think that laptop is(great pics, but it is still hard to tell)
the fabrication is possible, but really depends on how confident you are cutting up parts of your dash.
there are a couple of threads on push button start-- wagun(i think thats right spelling) has a very nice push start, so keep an eye out for that.
I think i covered the major issues,
most importantly, Have Fun!