Of course it can be moved up and down via the brass threaded rod, and wing nuts. Another view of the levitation stand. Without the additional magnets, the ring magnet would not have floated free of the carbon on both sides. Here one can see the copper wires from the commutator motor brushs are embedded in the carbon, and were simply cut off at the carbon surface. The embedded wires don't seem to affect anything.
Carbon does have a real temperature problem.
Even opening a door nearby will affect the height of the levitated magnet, depending on its weight.