Legal Question in Family Law in Florida

If you are listed on the birth certificate.

To have legal rights, by which I assume you mean time-sharing (visitation), you will need to establish your paternity through the courts by filing a Petition to Determine Paternity and for Related Relief. As a part of that process, you can ask the Court to order a Parenting Plan that includes time-sharing for both parties.

Mom basically has all the rights and decision making authority until you go through the courts to establish your paternal rights (custody/time-sharing).

Yes but it is not automatic, you still have to file papers with the court to establish and enforce your rights. Use of a lawyer is recommended.