I'm thinking the constant chewing and tearing might have something to do with weak nails.. I've never bitten my nails, and even if I tried to start up, I wouldn't do much damage because my nails are really strong and only break when they grow to ridiculous lengths and tear on something.
I definitely agree with moisturizing your hands every day, paying special attention to the roots of your nails. That's where they grow from, and they don't have their own supply of moisture- the root takes moisture from the skin around it, and if the skin is dry, the nails will be dry and brittle and crack easily. Nails also need nutrition, they're made from the same material your hair is made of, so eat whatever leads to healthy hair, and you should have healthy nails, too.

Don't wear nail polishes often, they'll turn your nails yellow after a while and they don't let the nail breathe properly. Nail strengtheners should be okay, though, for quick-fixes.