Answer:
I run up and down the stairs without moving. What am I?
Four fingers and a thumb, yet flesh and blood I have none. What am I?
Of the king I am blue and of the peasant I am red. Of the frog I am cold and of the dog I am hot instead.
I've been argued on my color. Without me you'll die. So many attempts on your life use me so make sure you have many of my White friends.
I only exist when you are here. Where you never were I can never be.
I stay where I am when I go off. What am I?