Yes When a very massive star explodes, it may leave behind a star of more mass than the Sun squeezed tightly together into a ball only about 16 km (10 miles) across. read more
It's thought that Neutron Stars are indeed composed almost entirely of neutrons, but may have 'quark soup' or other complexities. They definitely exist and some of them are pulsars. Too small to be White Dwarves - which are made up of collapsed matter, still normal atoms. read more
The energy source of the pulsar is the rotational energy of the neutron star. The majority of known neutron stars (about 2000, as of 2010) have been discovered as pulsars, emitting regular radio pulses. read more