or if they are in stress or if they hurt them self
Because your fingers could smell like food, or they could be getting irritated with you.
With Their teeth Maybe?
Yes, if an animal has teeth it can usually bite.
A hamster bites when: It is not yet familiar with you. If you are holding it in such a way it hurts him. If you are pestering him while he is asleep or eating. If he sees you as a threat.