For the first challenge, I'd say there's two options based on supersonic economics. The first is the "big market" case. Here, SSTs are somehow cheap enough to operate and secure overland flights such that they become fairly common. In this case, Pan Am would almost certainly buy some, but getting this case...well, I'm not really sure if it's doable. The other is the "tiny market" case, which is basically like the Concorde of OTL--only a few operators selling mostly as a high-cost status item, but Pan Am happens to be one. Maybe here the 2707 launches with Pan Am as a launch client, and like Concorde did it limps along in service for thirty-odd years before finally the airframes age and there's no interest in a replacement? That, or Pan Am ends up buying a couple Concordes it optioned IOTL, and sees a similar history to British Airways and Air France.
Having Pan Am operate spacecraft is...unlikely, unless they're fully reusable and there's a commercial market for launch of people to orbit in large numbers. Even a best-case in my estimate, though, sees a cost-per-kg of $200 or so, making a ticket cost about $24,000. That's at least achievable for rich tourists and maybe some businesses staffing LEO research outposts (or flying to powersats?) but I don't think the launch market will be large enough to interest a traditional airline--it'll probably be dedicated, much smaller spaceline operators.
I can't really address the third challenge since I don't really understand why Pan Am didn't survive deregulation well enough to try and find a PoD that changes that.
Suborbital refueling might get mankind an economical SSTO space transportation system to orbit long before Skylon (air liquefaction) VentureStar (impossible mass fraction) or X-30 Orient Express (scramjets)
Archibald, I think we've been through this based on my analysis for you elsewhere:
1) There's two vehicles, one that makes orbit and one that does, and a complex staging event in the middle with rendezvous and fuel transfer. That's two-stage, not single-stage.
2) A two-stage vehicle using the same level of technology can also be fully-reusable, easier to turn around, and have substantially larger payload.