In what ways can force be applied to a black hole Besides gravity I have never heard of another force pushing or pulling a black hole. Does an object falling into a black hole push the black hole when it crosses the event horizon? What happens to the kinetic energy of an object that enters a black hole?
Aside from gravity, electromagnetic forces can change the momentum of a charged black hole. 

When something falls into a BH momentum is conserved according to every observer, although they may have very different ideas of how that happens. A distant observer will see the new black hole as having some momentum and so moving in some direction relative to the trajectory of the old black hole. It's not really appropriate to describe it as pushing, though. From the object's perspective, nothing special happens as it passes the event horizon. From a distant observers perspective, the gravitational field of the moving object merges with that of the black hole, and the result is the field of a slightly bigger and slightly moving black hole.