Close. Everyone forgets that a neutron star is held together by gravity. Take a bit away and that bit will fall apart. Rapidly. Very, very, very rapidly. Like significant fraction of c rapidly. Imagine Mt. Everest suddenly flying apart at a significant fraction of c.
You mean like....ALL life on Earth? From a single teaspoon full? I doubt it. Would it kill the drunk camper who picks it up and decides to use it to keep his sleeping bag warm? Maybe.
We aren't talking about the outer parts we talk about a core piece, wich is almost as dense as a black hole because its only little away from becoming one.
"A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses..." as mentioned in Wikipedia
So the weight varies, and not every "specimen" would be that close to a black hole.