How likely am I going to be able to move with my children?

You need to petition for court order allowing you to move your children.

You need to speak with attorney as soon as possible.

Since child support can go back to date of filing of petition, you are not legally liable.

How do I go about adopting my husband nephew who lives in africa which his parents want us to adopt him and take him

You need to hire experienced attorney in foreign adoptions.

How often should a 16 yo be expected to do visitation in a month time?

It need to review the custody order to provide answer.

Can I take my child on a weekend vacation without permission?

Check custody order and see if taking on weekend vacation conflicts with order. If not, then take. If father does not visit as ordered, then go...

Can my husband do this?

You need to speak with attorney as soon as possible.

You can petition for modification based on his change of state.

I filed for sole custody, can I cancel it?

You can go to court and withdraw petition.

After serving my spouse she has not taken any legal action against me What can I do now ?

You can move for default and you need to speak attorney.