No. The father must be informed and given the opportunity to object.
Only with their permission. The custody order have to be changed in the court it was issued.
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.
when or why? Mothers will lose custody if they are found unfit by a family court
It depends on the law where you live and your custody order. If the father has sole legal custody (as opposed to physical custody) he would be able to make that decision without input from the mother. If legal custody is joint or the mother has sole legal custody, no he could not.
Grandparents don't have a automatic legal right to see their grandchild. It's entirely up to the parents. In some states a grandparent can petition for visitation and the parents will be heard as well and usually the court wont go against the parents wishes. It depends on the circumstances.
file for custody
Yes she can. Unwed mothers assume an automatic temporary custody, until the case is decided by the court. The only way to stop her from moving is to file for custody ASAP. Once filed, the state has jurisdiction and she can't move.
Your great-n uncle is either the brother of your great-(n-1) grandparent, OR the husband of the sister of your great-(n-1) grandparent, where 'n' represents the number of 'greats.' For example, your great great great great uncle (n=4) is the brother of your great-great-great grandparent or the husband of the sister of your great-great-great grandparent (i.e. your great great great great aunt's husband).
Only if you are 18
Courts will sometimes give custody of children to mentally ill or borderline mothers. It will depend upon the severity of their cases and they will be assigned social workers.
Sole custody is not common these days except for single mothers. see links
Single mothers have sole custody until the court rules otherwise, but in Texas you can get a jury trial.