Ultimecia's castle is in an another world(remember the portals?) and I think the dark thing in the left picture is a dark wind(remember when you walk in the halls were you will see the dark clouds moving? it only means that ultimecia's castle is in another world because you wont find her castle in the map and clouds only move's when a planet rotates it's axis, actually clouds doesnt moves but the planet does.

I think the reason why ultimecia's castle is floating because there is a dark matter below and above it(example: when you try to compel the north and south ends of the magnet and let go of the north side and hold the south end you will see that the north edge will float above the south end of the magnet) just like the castle of ultimecia.

Aren't you curious why there are chains all over ultimecia's castle?
Because it might get sucked-up by the dark matter(gravity) surrounding the castle.