Answer:
I am an animal named after the animal that I eat.
What is common to eat before it's born and after it's dead?
My first is in window but not in pane. My second's in road but not in lane. My third is in oval but not in round. My fourth is in hearing but not in sound. My whole is known as a sign of peace. And from Noah's ark won quick release.
A white horned symbol of purity and grace.
What grows up while growing down?
My days are numbered. What am I?