It has to be done before the move. Once out of the country, he's pretty much screwed as only one country honors foreign custody awards for fathers, Cuba. see link
I'm assuming you are the father and a fit parent and then yes, you would probably get custody.
Generally, custody orders end at age eighteen and the child can choose where she wants to live.
Grandparents do not have any legal rights to custody of the grandchildren but if you suspect the environment is bad for the child you should contact the CPS and then you can say you want to foster the child if the mother refuses to kick him out or move.
If she abandons the child, yes.
This is 100% up to the judge. To change the custody agreement or order requires a trip back to court. Would like to add however that moving in with the boyfrind as long as he is not a danger to the kids, is not something that normally changes custody. It's just moving on with life after the divorce.
Can, but as she moved away initially, a judge may not consider it.
Single mothers have sole custody, however I teach fathers how to stop such moves.
The mother can allow the child to live where ever the mother wishes.
what are you supposeto do if your boyfriend moves far away with his family?
If there are kids involved, usually the one who has custody which is usually the mother. Basically the one who has the biggest need for it. Also, often the one who asks for a divorce is the one who moves out.
With an injunction
The mother has the option to file for modification of the original custody/visitation order if the parent moves or even prevent such a move if state law has that provision, however the other parent has the right to respond to such a motion. Ultimately, the courts want to maintain involvement of both parents in a child's life. If the parent moves and maintains visitation as outlined in the original order on his own dime, there would be no reason to give the mother full custody. However, if the move would make it impossible for the parent to maintain visitation as originally outlined, a modification may be granted.