A neutron star is relatively massive and extremely dense, which is why they have a tendency to attract matter from their companion stars—remember that most stars are part of binary systems or systems with even more stars, so there is a distinct possibility of this happening. read more
The limit of that pressure is known as the Tolman-Oppenheimer-Volkhov limit, where neutron degeneracy pressure would fail, and the neutron star would collapse to a black hole. read more
A star can either become a black dwarf, neutron star, or a black hole. Main sequence stars like the sun become a red giant by fusing helium. Then, the star ejects its outer layers, leaving an inner core of extremely dense matter supported by electron degeneracy pressure. read more
Yes, the center of a neutron star is much denser than the surface material, because it is under greater pressure. The limit of that pressure is known as the Tolman-Oppenheimer-Volkhov limit, where neutron degeneracy pressure would fail, and the neutron star would collapse to a black hole. read more