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The other answers cover your second question well enough, but there's some detail still missing on the first one - what happens to the protons and electrons in a star when it collapses into a neutron star. The basic answer is simple: they become those neutrons. The reason that this happens is that, as it turns out, an {electron, proton} pair is sort of ...


You don't say at what level you are studying this. Before you get stuck into the intricacies of exotic neutron star equations of state you need a good grounding in statistical mechanics and nuclear physics. A good place to start is the first few chapters of Shapiro & Teukolsky; "White Dwarfs, Neutron Stars and Black Holes" ...

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