It would be very wise to have something written down on paper. Just make the buyer sign a piece of paper saying he/she's buying it for a specific dollar amount, and buying it 'as-is'. That way if it completely falls apart 1000 miles down the road because they abused it they can't come after you.
Yes, remove the plates. My brother sold a car a few years ago and forgot to take the plates off. He was really upset when the new owners started parking in no-parking zones and the tickets were being mailed to my brother, and in his name.
I don't know about selling out-of-state as I've never been in that situation before.
