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Ignore pulsars and the like, just a neutron star in empty space – does it emit light and neutrinos?

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Neutron stars do indeed shine and some like this one have been observed in visible light. Like white dwarf stars, if they were scaled up to be the size of the Sun, they would outshine the Sun and most other stars in the galaxy. It is only their small size that make them hard to observe.

As for neutrinos, it seems they do too. This link might help explain neutrino activity in / from neutron stars further.

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  • $\begingroup$ Do they emit as black body? $\endgroup$
    – Alchimista
    Commented Nov 10, 2017 at 12:11

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