Answer:
I can move even when you are still. I can be one or many.
When I live I cry, If you don't kill me I'll die.
Covered in stone and sun. It's home to many but also none. What is it?
What is that which, though black itself, enlightens the world without burning?
Lovely and round, I shine with pale light, grown in the darkness, a lady's delight.
If it’s information you seek, come and see me. If it’s pairs of letters you need, I have consecutively three. What am I?