If there is a court order that says not to leave the state of course you can not leave!
Yes, with parental consent.
Check with your lawyer, and check you custody agreement.
Provided it is just for a trio or vacation, and not a permanent move, then possibly yes. In other circumstances no. It depends a lot on marital status, legal custody, and any existing court orders. Consulting a lawyer would be a great idea to find out the legalities for your specific situation.
No. I believe that you need the father to approve before you leave
Provided there's not custody order in place.
This is dependent on individual state laws.
I'd say she can unless ordered not to do so.
No she absolutely cannot do that. In fact, wherever she lives, she isn't legally authorized to leave the state with those kids WITHOUT your written consent. If you agree and it's in writing, she can take the kids to another state and, no matter where they are, child support still applies.
A lot of fathers leave because the pressure of having a newborn and a potential wife is too much. Keep in mind that if you are thinking about having a baby with him, TALK ABOUT IT!!
Leave permanently, no. That would violate the visitation order. To move would require his and the courts consent.
Yes. Well most of the time she can but sometimes she cant it depends why she went to jail