No you cannot. The defendant will need to be personally served with process, unless the defendant will sign an acknowledgment of service. Where does the child live? GA or CA?
When married the name in which the property is titled, is generally irrelevant to the property division. When not married, the name on the title essentially controls. The short answer is it is his vehicle, not yours. What you can do is seek a child support order.
You say you were served on 11/6/2021. That you filed an acknowledgment of service after that, why you did that I don't know, but that filing does not change the date you were served (11/6/2021). Thus your answer came due on 12/7/2021, and your time to open default as a matter of right would have expired 15 days later, on or about 12/22/2021. It sounds like your answer was in fact filed late and you do not mention filing a Motion to open default as a matter of right. You may still file a regular motion to open default, the basis on which the court may grant that are limited (unlike the motion as a matter of right). None of this has anything to do with the merits of the case, but only procedural compliance.
The time to demand a DNA test came and went a long time ago. The time to do that was at the time of the child support case that produced the child support order. If you were properly served with process in that case and then you never responded or appeared, paternity was thereby established, despite there being no actual DNA test. Those SSDI benefits are not subject to every type of garnishment, but they are subject to child support garnishment. The arrears, you owe until paid in full, they cannot be waived or erased. If the monthly SSDI benefit to the child with an ongoing child support order is not more than the child support amount you are ordered to pay, then you owe the difference.
You may have a claim against him for wrongful eviction. I do not believe you have a viable claim against the PD. Is he the father of any of the children?
A contempt case is filed in the county/court that issued the order that enforcement is sought. When you relocated, depending on various factors, you should have modified the current order. If your relocation is impeding the other parent's visitation rights, then you gave them a claim for contempt, because you did not modify the current order.
Your agreement with him is not legally enforceable. In GA the parents do not have the right to waive the child support obligation. You need to modify the current order for him to be ordered to pay you child support, and the arrears you owe him, you still technically owe him.
Child support is based on monthly factors. You pay the entire monthly amount for the last month the child is entitled to the support. Will the child also be graduated from high school when turning 18? Most orders state that child support shall be paid until 18, unless still in high school, then for longer but not beyond age 20 if still in high school.
While married and no divorce pending, you cannot legally force her to leave hers and your residence. You cannot "evict" her. If she will not leave voluntarily then you need the divorce court to intervene and the judge can order one of you to leave.
The issue of who will get the car will be decided in the divorce case, perhaps on a temporary basis, but definitely on a permanent basis..