Answer:
Face with a tree, skin like the sea. A great beast I am. Yet vermin frightens me.
It has plenty of backbone but doesn't have a let. It peels like an orange but it comes from an egg.
I am orange with black stripes and known for my fierce roar. What am I?
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.
When they are caught, they are thrown away. When they escape, you itch all day.
What do you purposefully put lots of in and on your body, but run away from when you encounter it outside?