Federal courts are courts of limited jurisdiction. That means, their power to hear cases is deliniated by the Constitution. If a case falls outside of the requirements set forth in Article III of the Constitution, a Federal court cannot hear the case. The three "requirements" are: Jurisdiction (is the court permitted to hear the case), Standing (do the parties have a right to bring the claim to the court) and Controversy (there must be a dispute to be litigated). Now, these are the very basic requirements. Congress has the authority to further define each of these elements for the Federal courts, as well as, the Federal court's themselves.
On the other hand, state courts are courts of general jurisdiction. This means a matter can always be brought before a state court. Whether or not the matter can remain in state court is another question.
Court of Appeals
Not necessarily - just someone who is admitted to practice before the court in question.
Most federal cases begin in the district courts.
United States Appeals Courts, if by Federal you mean the Supreme Court. Otherwise, the chain goes- Local -> Appeals -> Supreme/Federal Court
federal district court, federal court of appeals court,and the U.S. supreme court.
The Federal Court System gives the people a neutral ground to have their appeals heard. It also claims original jurisdiction over cases between states.
The most likely first step would be a hearing before the U.S. DIstrict Court for the Federal District in which the state is located.
Satisfied in what manner?
Federal trial courts almost always have original jurisdiction in the federal system.
Any court, even a lower state or federal District Court, can find a federal law that is relevant to a case or controversy before that count unconstitutional, if the court has a rational basis for making such determination. These cases often end up being petitioned to the US Supreme Court for a definitive answer.
There is no federal juvenile court
No. Before the court enters an order for support, it determines paternity. Apparently, the court was satisfied at the time that you were the child's father.