While you can't build a CAR, you can certainly build a working replica.
There is some manufacturer who makes fake flash suppressors. It's pinned to the barrel (or maybe welded) but the milled slots for the flash aren't milled all the way through. Thus, you have the appearance but not the function. So long as it's not screwed on the barrel (threaded barrels are a no-no), it's perfectly legal.
Concerning the stock, you can get a pinned stock from GunSmoke Enterprises. It looks like a collaspable stock, but is pinned such that it won't collaspe and the positioning holes are permanently filled such that even if the pin is drilled out, there's no way it can function except closed. Phony like the muzzle faux-muzzle brake, but it's a CAR-15 lookalike which shoots.
Hope this helpless information helps.