Answer:
I run up and down the stairs without moving
I am a precious stone, as clear as a diamond. Though you can walk on water with my power, try to keep me, and I'll vanish in an hour. What am I?
I am black within and red without; with four corners round about. What am I?
Taken from a mine and then locked up in a wooden case. I am used by students everyday.
My first though water cures no thirst my next alone has soul and when he lives upon my first he then is called my whole.
What gets bigger the more you take away?