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
I am not a queen either, neither I am a clown
Teeth are neither kings, queens, nor clowns, but they do sometimes have crowns
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!