for sure invest in the carproof.
the three tires is odd as all hell. most likely (since it's on rims), it curbed/potholed and damaged the rim and tire. but if it's steelies, easy enough to buy one wheel and tire for 150 bucks to match.
deal seems good. for the test drive, what i suggest is bring your dr. license, a copy of your current insurance, ownership (if you happen to have a car now) and leave copies with them. if they have a big issue with that, then they really shouldn't be selling a car privately.