Answer:
the only amusing part of the body
I come off of a beautiful creature which soars in the sky. I come off of a peckish creature which has a tail as mighty as the sun! I am sometimes dirty and parents beg you not to pick me up.
I produce wool and spit a lot
Two bodies have I, though both joined in one. The more I stand still the faster I run. What am I?
What tastes better than it smells?
I always have to work with something in my eye. What am I?