does ultraviolet light shine 24/7
depends on what side of the Earth you are talking about, because UV rays come from the sun, and are absorbed by the ozone inside the atmosphere. The sun is always shining on Earth, just opposite sides
It takes about 8 mins for the sun's light to reach us. So I am assuming that it doesn't. Or at least not directly. Maybe bouncing off of the atmosphere, or the moon. (But those are just wild guesses)
Natural? At Day, totally, at night, too much less, only that can be reflected by the moon. Obviously, at night when the moon is present. And finally, cosmics rays, from far away stars. Think about. If you can see the light from the stars at night, there is light that you can't see, ultraviolet light...
Not sure exactly what you are asking. UV is just like any other solar radiation - the sun produces visible light, infrared, and UV all the time (the sun doesn't turn on and off). But there is no natural UV light at night on Earth (there is artificial UV light from TVs, computers, building lights, etc.) since there is no solar radiation reaching the night side of the Earth.
