No, not if your mother has sole physical custody. If there is a joint custody arrangement, you'd still need the cooperation of both parents to make it happen.
Only if you are 18
no
yes you can because you are moving to a family members house
Only with their permission. The custody order have to be changed in the court it was issued.
No.
30 miles
It depends how old she is and she should at least let him know
No you can legally move out when you are 18 no matter what state you are in.
Definitely,decisively,with a strong emphasis on the part 'without your mothers'.Mine fathers don't live, it is a reason and causae of mine version.
You can move out if your parents house whenever you please but you have to have their permission and somewhere to go. Unless you are 18 or over.
Not unless you were married (parental approval), or by court order.
That is dependent of custody orders, but even without, the other parent could file an injunction.