What Am I Riddles

Question: Old mother twitchet had one eye and a tail that she let fly and every time she went through a trap she left a bit of her tail in the trap.

Question: What has teeth but can't bite?

Question: Always old, sometimes new. Never sad, sometimes blue. Never empty, sometimes full. Never pushes, always pulls.

Question: I am duplicate of you, but only lighter. What am I?

Question: Wind and cord combine, buzzing in the box. In all this we find, though to some the use is lost. What am I?