Am I financially responsible for a child's behavior?
Yes, you are financially responsible for any child under your care in most cases. Just as a parent would be, a guardian will be held accountable for any damages or harm due to the child's actions, including any medical bills the victim may have.
Can I move outside California with the child?
You cannot move with the child outside the state of California without first obtaining permission to do so from the court. If you get permission from the court, you must establish guardianship in the state that you plan on moving to because different states have different laws pertaining to guardianship.
Can the child stay with his/her parents or anyone else, even if it's just temporary?
The child must stay with you and only you unless the court has given permission.