Talking of what is real and presumed real ,I read once that retiring presidents get a last ride on Air Force One, now the story I had read somewhere was that when LBJ got back to Texas he had a crew virtually strip the artifacts from the plane for his presidential library, wondering is it true or hooey? and yes this Canadian follows with great interest your leaders and history...
It is true that LBJ expected all the "goodies" from the plane to be offloaded as his own personal property once he was flown home after Nixon was sworn in, although they didn't accommodate him as it is government property, not his own personal property. This is documented in a book entitled "The President's Club", and I don't doubt it at all.
I do believe that all retiring presidents are flown home in the plane known as Air Force One, although it only uses the call sign Air Force One when the current president is on board. Since the former president is no longer in office, the plane just goes by SAM (Special Air Mission) and I believe followed by the tail number when the current president is not on board.
Nixon was even flown home after he resigned from office, and once Gerald Ford was sworn in, the call sign was immediately changed from Air Force One to SAM (tail number) over the central U.S. Once they landed in California, Nixon requested a photo of all the staff and crew.
When a former president dies, the former first lady (if she still survives) gets flown from her home to the state funeral in D.C., and they try to reconfigure the plane to as close as possible to how it was when her husband was in office. For example when Ronald Reagan died, the current jet used as Air Force One flew her from Simi Valley CA to D.C., and they even had Reagan's flight jacket draped over the presidential chair, and arranged it as much as they could like it was when Reagan was in office down to a jar of his famous jelly bellies.
Regarding presidential limousines, I'm not saying this car that is being advertised wasn't used during the Kennedy administration, but I have seen a TON of footage of JFK and do not recall ever seeing him in this car. I've seen him in many vehicles, even a couple still photos of him in the secret service followup car known as the Queen Mary (which was a Hess & Eisenhardt build), but most often in the car with secret service designation SS-100-x, AKA 100-X, which he was assassinated in on 11/22/1963.