Answer:
I have many feathers to help me fly. I have a body and head, but I'm not alive. It is your strength which determines how far I go. You can hold me in your hand, but I'm never thrown.
This thing runs but cannot walk, sometimes sings but never talks. Lacks arms, has hands; lacks a head but has a face.
Don't do this in the shallow end.
I hide but my head is outside.
My first is equality; my second is inferiority; my whole is superiority.
The warmer I am the fresher I am.