From what I understand about the uncertainty principle, the more
you know of an object’s position, the less you know of its
direction/velocity…and vice versa.
Does this apply to black holes too?
With a fixed position (right?), its intense gravity would keep its
direction under control as well?
No as to both.
Black holes are (usually) quite massive objects, probably ranging in size from about 2.4 solar masses to entire galactic cores. However, with one exception I can think of, black holes move just like any other object. They’re still subject to special relativity and don’t have a “fixed” position. They have measurable velocity vectors just like every other object. In fact, most or all of the ones we can observe are orbitting a companion.
In any case, the uncertainty principle isn’t particularly applicable to something as massive as a black hole on a macroscopic level. The uncertainty in position would always be less than the planck length.
What Truth Seeker said represents our current understanding. But I feel I should mention that until gravitation can be expressed in quantized form, it’s all rather speculative.