Answer:
I am an animal named after the animal that I eat.
What has a brown coat, a long tail, and lives in house or shed but most active while you're in bed?
This noble creature has the embarrassing inability to get up once it's been flipped onto its back.
What two animals do you take to bed with you?
What's the red stuff between elephant's toes?
They are many and one, they wave and they drum, Used to cover a state, they go with you everywhere.