I got my foot hung in a wall-mart speed bump and broke tibia in left leg august 8th and their denying my claim what happens now

You need to retain an attorney to rep[resent you. Without an attorney you will not be treated fair. Retain an attorney today.

Do I need my daughter's father permission to hyphenate her last name by adding mine?

You would need to contact him for a minor's name change. Please be mindful that you can not just add your name to the child's name. In order to...

My girl's father is petitioning for legitimation, child support, custody, and visitation.

You need to retain an attorney to represent you. Based on what you stated in your post it appears that service was proper.

How do I go about getting papers by mail and what's the cost of a divorce?

Not sure of what papers you are speaking of but if you are speaking of divorce papers, you do not get them by mail. The cost of a divorce vary...

Will my son have to serve time for aggravated assault?

He is charged with a serious crime. You need to hire an attorney to represent him.

Down payment to dealership?

They should give you your money back. If they do not file a small claim action.

Unless otherwise ordered by the court, in Georgia grand parents has no rights.

There are too many unanswered questions here to provide you with an answer. You need to go and sit down with an attorney to fully discuss the matter.

What should I do to move the process along?

Short of hiring an attorney to represent him, there is nothing else you can do.

Clearly you can not do this by yourself. Hire an attorney to represent you.