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Yes, it is perfectly possible to move a black hole, in any reasonable sense. In particular something that is important to understand is that, far from the event horizon, black holes are not particularly special. The gravitational field of any spherically-symmetric distribution of mass is the Schwarzschild solution in the region where there is no matter for ...


Your question doesn't make much of a sense to me. Your frame of reference is everything. I can view it in such a way that it would look as if it was accelerating, and it also may seem to be stationery in some other frame. Don't mess with motion in space unless your are able to find a reference ponit.


In addition to what @Jack Mazy said about force due to gravitational attraction, there are also charged (Reissner–Nordström) black holes. I would imagine in theory you could take another charged object and place it near the black hole which would cause Coulomb force on black hole putting it in motion.

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