I thought the downvotes were unjustified until I got to the last para. And if you'd phrased that as a question, you'd've probably got away with it; people have itchy trigger fingers in a thread so filled with BS.
In answer to your first question: a big enough neutron star always becomes a black hole. In fact all matter wants to collapse into a black hole, but there are repulsive forces that stop it: the electric "Coulomb" forces between molecules and atoms are enough to keep you human; in something as massive as a star, the temperature of the plasma pushes back against the collapse, and in a neutron star its the "degeneracy pressure". But if you exceed a critical mass (Tolman–Oppenheimer–Volkoff limit), then even that won't stop it.
I don't follow what you're asking in the second question. But a change in the position of matter is a change in the gravitational field, and the changing field has its usual affect on remote objects.