Answer:
Take off my skin, I won't cry, but you will.
I fly through the air on small feathered wings, seeking out life and destroying all things.
Halo of water, tongue of wood. Skin of stone, long I've stood. My fingers short reach to the sky. Inside my heart men live and die.
Long and think, red within, with a nail at the end.
It has no top or bottom, but it can hold flesh, bones, and blood all at the same time.
Those with eyes bigger than their stomach will definitely leave the restaurant with one of them. It is named after a house pet as well.