No. The mass of a neutron star is so compact and the gravity so high that it could never again become a regular star. Besides, neutron stars come from the cores of stars that have already gone nova. All the hydrogen was already fused into heavier elements.
Any two types of star can be gravitationally bound with another for instance you can get neutron-neutron pairs you can get two yellow stars or you can get a red super giant with a normal star so long as they are in gravitational equilibrium any two can be a paired star
Neutron stars do not have fuel. A neutron star is a remnant of a star that has already died.
Not exactly, while a pulsar is a specific type of neutron star (that being a "spinning neutron star") and a binary system is a pair of stars orbiting each other, a pulsar does not need to be part of a binary system. It would be possible, however to have a binary system with one of the pair being a pulsar and the other a neutron star (assumed to be the non-spinning or "normal neutron star" variety).
A subgiant star is larger than a neutron star. Neutron stars are incredibly dense and compact remnants of massive stars, while subgiant stars are in a transitional phase between main sequence and red giant stages, typically larger and more diffuse than neutron stars.
It would not exist. A neutron star is what it is by virtue of the mass of the whole star. Extracting just a pinhead would revert that matter back to normal matter. For the sake of density - as weight has nothing to do with matter outside of a gravitational body. The denisty of a pinhead of neutron star would be the equivalant of about 100 times the mass of the Great Pyramid of Giza
Pulsars are not only a kind of neutron star, they are neutron stars. See related question.
A star that becomes a white dwarf simply does not have the mass to become a neutron star. White dwarfs are the the remnants of a star very similar to our own sun in mass, where it takes a much more massive star to create a neutron star, Like the star Betelgeuse is a prime example of a star that does not have the mass to become a black hole but is massive enough to become a neutron star.
Yes, both black holes and neutron stars are remnants of the death of massive stars. Neutron stars form when the core of a massive star collapses but does not produce a black hole. Black holes are formed when the core of a massive star collapses beyond the neutron star stage.
It is still called a neutron star. Depending on how we observe it, it may also be called a pulsar.
There are no moons around a neutron star. A large, spherical body orbiting a neutron star would be considered a planet.
Neutron stars rotate rapidly due to their conservation of angular momentum. When a massive star collapses into a neutron star, its core spins faster as it contracts. Since angular momentum is conserved, the neutron star continues to rotate rapidly as a remnant of the collapsed star.
Neutron stars are born from massive stars collapsing, which conserves the original star's angular momentum. Since the original star had a slow rotation, the neutron star that forms from it will have a faster spin due to the conservation of angular momentum.