Process on a state prisoner is the same as you would serve process on any other person. I would advise that you contact the sheriff's department in whatever county the prison is located and arrange effectuating service through them. The Florida court has the power to dissolve a marriage even if the respondent is not a resident of the state of Florida and the court has no personal jurisdiction over the respondent so if that is your only issue the process should be relatively easy.
In accordance with Florida Statute, evidence that a parent has been convicted of a misdemeanor of the first degree or higher involving domestic violence creates a rebuttable presumption of detriment to the child; although it is unclear from your question whether any charges were filed resulting in a conviction. Regardless, the court will base it's determination on the best interests of the child. I would recommend seeking help from a parenting coordinator or the appointment of a Guardian Ad Litem.
You can file a motion for continuance and set it for motion calendar before you leave. Alternatively, you can ask your ex if he would be willing to allow you to appear telephonically and submit an agreed order as to same. Unless your father is an attorney, he cannot represent you at the hearing but you can hire a coverage attorney for the hearing in the capacity of a limited appearance for same.
Mediation is always the best way to go, if possible, because then the fate of your circumstances is in your hands rather than a stranger. If your ex will not agree to try mediation again you can motion the court to compel same. Further, if you are unrepresented you are free to communicate with her attorney and he or she should apprise you of exactly what your ex is seeking. If the attorney refuses to discuss the elements of the case with you, you can file a request for a case management...
He will have to be served regardless. If you don't know where he went you will have to perform a diligent search, and certify same with the court, before you attempt constructive service. You should get the form for the diligent search from the clerk so you can begin looking for him. However, since he has been gone such a short amount of time I would suggest you call his friends and family and give him a few days to resurface. You have 120 days to serve him after filing.
It is always better to work things out and if you can do so on your own, while saving costs associated either with litigation mediation while minimizing attorney's fees, you should take every opportunity. However, unless your girlfriend presents a danger to your child your ex has no legitimate basis within the parameters of the law, to make this demand.
Do you have a temporary support order or was the amount agreed to by you and your husband? If the latter you can either file a motion for temporary support (unless it was mentioned in your petition or counter petition), then you can just request an evidentiary hearing. If there was no order in place, you are always eligible for retroactive child support for a period of up to 24 months since you and your ex were living together.
Not providing full financial disclosure (or being afforded the same) can be enough to set aside a pre-nup. Duress would have to be proven based on the circumstances leading to your allegation. For example, timing is a relatively easy way to prove that you were under duress (ie if it was signed a few days before the wedding), but in most cases one would have to look at the specific facts surrounding why you are claiming duress.
If you feel you did not get a fair chance to present evidence you can file a Notice of Rehearing within ten days of the order. You should have also gotten an opportunity to review the documents your ex submitted.
If he is paying child support as the result of a final judgment in a paternity action then the parenting plan should have outlined a timesharing schedule. If the mother is in violation of same, you can file an enforcement action to effectuate timesharing. If child support is being paid voluntarily, you should immediately file a paternity action to establish a timesharing schedule and official child support payments. If the latter, hopefully he has kept receipts of payments so that he can...