The judges are bombarded with text messages and emails every day in family law cases. I always tell my clients that your evidence (in this case, the texts) must tie to some issue in the case in order to hold significant weight. His communication is disappointing, but not uncommon. Unless there's something to do with the children, him being unpleasant and rude won't effect the case much.
Most courts have a way for inmates to appear by phone for hearings. You should contact the judicial assistant for the judge who will preside over his hearing and see what the procedure would be to appear by phone.
This depends on whether the mediation was set up through the Courthouse or with a private mediator. If it was through the Courthouse, you should be able to call the mediation department to obtain a new date. If it was a private mediation, you can file a Motion to Compel Mediation if you feel that is proper. Set it for hearing and have the judge order a date certain for the mediation.
You can certainly ask for sole parental responsibility but it will not have much to do with the lack of child support. The sole parental decision will be based on what's best for your child. If he has been in and out of prison, that would certainly influence the Court's decision on whether to award that to you.
I would definitely have a few consultations with some appellate lawyers to see what your chances are on appeal. A stay of a money judgment will require a bond and the trial court will usually not stay or abate support payments.
As discussed above, the trial Court has a vast amount of discretion in family law cases and appeals are extremely difficult and costly. Paying for a transcript of your trial may set you back more money than you expect.
A Motion to Set Aside or Motion for Rehearing would have to be filed within 10 days of the issue date on the Temporary order. Be careful though, if you're filing based on rebuttal evidence that was known to you at the time of the hearing, it wouldn't be grounds to set aside the order. There has to be some evidence that was unknown or couldn't have been known at the time of the hearing.
It's a difficult question to answer and I don't think any attorney could predict with 100% certainly what a Judge would do even if we knew all the facts. Your GAL will be very helpful in the case but I share the same concern about whether your GAL is qualified to render a psychological opinion. If your GAL is not a psychology expert, than your wife's psychiatrists may hold greater weight.
The way my firm typically handles these situations is that we use a Private Investigator to conduct a dilligent search for the individual. A PI typically has access to more databases than a lay person. We usually then have the PI file an Affidavit of Dilligent Search detailing their efforts. Service by publication is complicated so you should certainly have an attorney help you with this issue.
The only thing I would add is that the Florida Bar Rules prevent an attorney from taking a family law case on a contingency, so that is why any family law attorney will and should take a retainer fee up front.
Be careful though...even if the Court awards attorney's fees, they are usually not lump sum and the person paying is often given generous payment terms.