Answer:
Soft hairy from door to door. I am the pet that always stays on the floor.
So cold damp and dark I am. To stay you would refrain yet those who occupy me do never complain.
I pass before the sun, yet make no shadow. I'm all around you, but you cannot see me. What am I?
What begins with an E but only has one letter?
I am the kind of a tree that is carried in your hand. What am I?
When you take away the whole from me there is always some left.