Diagnose first. The first thing to do is have her evaluated by a behavioral psychologist or psychiatrist. there may be treatment alternatives that can successfully manage her behavior. A last resort would be a psychiatric hospitalization to further the evaluation.
Maybe. Not usually unless they are at risk of hurting themselves or others. Therefore physical violence that escalates to that level may indeed necessitate admission to a psychiatric evaluation and inpatient admission.
Depends. Laws differ in different places, but where I am a person can not be forcibly hospitalized unless they present an imminent danger to themselves or others. People are not hospitalized, nor should they be, for throwing themselves on the floor, kicking and screaming, which is usually what is meant by "temper tantrum." people who have self control issues might benefit from counselling.