yes
Mother has sole custody in every state except Arizona. see link below
Law enforcement at least until a hearing is obtained. Then, the judge.
One would think that there would be a court hearing scheduled in which the parents from both states would attend.
No, legally a minor has no choice in the matter.
Only if there are grounds for concern for the safety of the child, or that the parent will run.
NO, until you are of legal age (in all states it is 18) and your parents have custody you can not do this, if you have reason and your sister can afford it you can ask your sister to have a custody hearing to switch and then you can.
They would have the right to request a custody hearing. A temporary injunction or other court order could be issued, removing the child from the home, but permanent custody would depend on the outcome of the hearing.
The parents have assumed joint custody.
Joint custody is a court order whereby custody of a child is awarded to both parties. In joint custody both parents are "custodial parents" and neither parent is a non-custodial parents, or in other words the child has two custodial parents.
Only can speak for Arizona: when the parents are unmarried, the dad has no rights except to pay child support. Of course if the child is old enough and the mom does not object, the dad can keep custody.
their parents
The mother. If she dies, her parents get custody.