Your last one is a good question. I don't have an answer but I was leaning towards some sort of conservation law (e.g. normal stars have magnetic fields, when they get squeezed down to a neutron star those fields must go somewhere and it will be very much "concentrated"). Apparently this is a bit too easy (didn't expect to be nothing different). Wikipedia provides a reference to a not too recent (2003) survey, namely this one: https://arxiv.org/abs/astro-ph/0307133 . I don't know if it's the state of the art but it surely is interesting.