What is the spiritual purpose of a white quartz crystal?
It's not radioactive, if that's what you wondering.
Yes. The glow in the dark property is phosphorescence, not radioactivity. The quartz (usually artificially made by hydrothermal process) has invisible impurities in it which absorb light to excite their electrons, which slowly fall back to ground state emitting green or blue photons. So it glows for a while in the dark.
Depends on your definition of safe. If you had a big enough chunk and hit someone over the head with it, it wouldn't be safe. Or you could trip on it in the dark and fall down the stairs - that wouldn't be safe either.