Answer:
I have one, you have one. If you remove the first letter, a bit remains. If you remove the second, bit still remains. If you remove the third, it still remains.
I am seen in the water. If seen in the sky, I am in the rainbow, a jay's feather, and lapis lazuli.
What goes through a door but never goes in. And never comes out?
What is put on a table, cut, but never eaten?
What measures out time until in time all is smashed to it?
What do angels sing in the shower?