If the energy used to accelerate the object was already stored in the system to begin with, then that system was already a black hole to begin with. If the energy used to accelerate the object was added from some external source, then the system would become a black hole simply because you poured a massive amount of energy into it.
Kinetic energy is not "in" the moving object. Its "in" the relative motion of two or more objects. Consider that you cannot extract kinetic energy from an object that happens to be moving relative to you
unless you use some machine to extract it, and that machine must connect to the object AND connect to a massive object stationary to you.
No, because of the previous answers.