Suppose it was somehow possible build a runway at FL300. Yes, doing so would be incredibly expensive, and it would be a mammoth civil engineering task, and the downsides would probably by far outweigh its advantages in practice; but for the time being, let's say that the desire to do it exists, and the issue of money has been resolved (as if by magic).
Let's also ignore the issue of getting the passengers, cargo, etc., to and from the actual aircraft, and focus on the aircraft operation itself.
Having constructed this runway-in-the-sky, what difficulties, compared to a similar runway built at ground level, would pilots and airplanes face when using it to "land" (if we can even use that term here) and take off, respectively, with a typical passenger jet (turbofan) aircraft?
It has been suggested that this is a duplicate of Would building an airport at 30,000 ft save money? (which also, in the question body, allows for one at 10,000 ft). I believe that this question is not a duplicate of that one because that question focuses on the cost of building such an airport and the savings in fuel expenditures because airplanes would already be near cruising altitude, while this question focuses on the challenges of landing at and taking off from an extremely-high-altitude airport while specifically ignoring the economic aspects.