I think you are a:
I live in a palace where it's dark inside
No light in there, unless open wide
Teeth live in mouths, which fit this description
Even though I am not a king, sometimes I wear a crown
Teeth sometimes have crowns
I am not a queen either, neither I am a clown
Obviously teeth are neither queens nor clowns, but I'm not sure if I'm missing a more specific connection here.
I'm known for tearing stuff by moving up and down
This describes chewing food
Don't take care of me and I might hurt you
If you don't brush and floss your teeth, they'll start to hurt!
Take care of me and get better pictures of you
People like to have a dazzling white smile for photos!
Without teeth, it would be harder to eat, which would definitely make life hard!