Can my wives new attorney call my mother and tell her everything he was filing and what his plan was?

A default is not a good thing you need to retain a lawyer asap.

How do I transfer my divorce from NC to FL?

You have to get a certified copy of the out of state order, register it here, then reopen the case. Use of a lawyer is recommended.

In state of Flordia I have custody 1/2 with the children's mother...we were never married.

If things are not working out then go for full custody. Use of a lawyer is recommended.

Just cause my child has her father's last name dose he have any rights even if he didn't sign the birth certificate?

He has no rights until such time as he establishes them. With that said you should petition the court to get child support. Use of a lawyer is...

Are my student loans that I incurred during my marriage considered marital liabilities?

Yes they are marital liabilities, the judge will make you pay them because they are yours, Use of a lawyer is recommended.

Do I have any rights to the house or furniture?

He cannot just kick you out he needs a court order. Use of a lawyer is recommended

he was appointed a public defender and a a guardian ad litem was appointed to the case.

What rights?

If not married he has no parental rights until such time as he enforces and establishes them.

As the custodial parent do i have the right to ask the identy of boyfriends and friends the noncustodial parent has with my chil

If you have an order that has those restrictions then yes you are entitled to know who the child is exposed to. Use of a lawyer is recommended

What do I file to get my ex to file his financial affidavit?

File a motion to compel discovery. Use of a lawyer is recommended