Yes, FSAE cars are property of the school and in many casses property of some other sponsors as well. They are junk after they are used. Some teams strip them down and just make new frame and body. The things you can buy from those kind of teams is frame, suspension and thats pretty much it.
It be easier to buy full plans from someone that did it couple of times. And with their assistence build one. I would guess cost wont be too high, couple of cases of beer and about a grand and I would sell my plans :) Would even help build it, for free food and beer and a bit more cash. (college students have low expectations as they get closer to graduation)
I would recommend buying plans from 2nd year or 3rd year. or improved 1st year cars. You don't want later year cars. They are too complex to build with basic tools.
From my experience, most of my first car was build using nothing more that grinders and basic tools. Only things machined where stub axles, hubs, diff casing, part of the uprights, steering rack and some other minor parts.
I would see only a problem getting differential. Since good amount of teams use Torsen T1 University special, its a replica of Audi central diff.
The diferential can be only purchased through "Purchase order" through school.