yes
One could also term it temporary alimony, it is a form of support.
No. The dissolution of a marriage and the financial support of one's biological children are two completely separate issues.
Divorce and domestic violence are separate issues. Not signing the divorce papers may not prevent the wife from getting the divorce and won't change any of the orders of the divorce such as property distribution, child support, etc.
Child support is a separate issue.
If it was a part of the divorce papers, there should have been a separate child support order, unless the divorce is more than 30 years old, predating the Federal Child Support Enforcement Act. Under those circumstances, it would be unenforceable.
The order would be retroactive to the date of separation. see links below
If the divorce decree addresses child support and is issued after the child support order then it replaces the child support order. If the child support order was issued or amended after the divorce decree then you abide by the most recent order with regard to child support.
If there is a court order for visitation or custody it is illegal to not follow the court order. Child support, custody and visitation are 3 separate issues in court. Paying child support or not is not a reason to take away the child's right to see his/hers parent.
I believe the spousal support decision by the court in the divorce decree would take precedence here .
This depends on a sole factor of whether you have a divorce decree or not. If you do not then there is nothing illegal about it; however if you do your divorce decree (or child support agreement) dictates where you may bring your child on a permanent or temporary basis.
Child support? Yes, but custody is a separate issue and children deserve both parents.
You need to check the provisions in the separation agreement and divorce decree. In some case they are addressed separately in some they are not. It often depends on the skill of your attorney.