Does anyone "know" this '68 Barracuda fastback?

Don't take this wrong, but,,,, I'm lost as to your question unless you are looking for past ownership or numbers history? If your interested in the car and you have inspected the car and are happy with what you see, what more is there to ask? You either like the car, accept the price and do the deal, or you walk. What I can tell you about the car wouldn't and doesn't matter.
Good luck with the buy.