I like the Federal Judiciary system of the U.S
Yeah, the federal judiciary of the United States is one of the three co-equal branches of the federal government of the United States organized under the United States 
Yes that is true. They are are independent system from other arms of government ( executive and legislative)
generally hears appeals from the courts of appeals and sometimes state courts, operating under discretionary review, which means that the Supreme Court can choose which cases to hear, by granting writs of certiorari. There is therefore generally no basic right of appeal that extends automatically all the way to the Supreme Court. In a few situations (like lawsuits between state governments or some cases between the federal government and a state) it sits as a court of original jurisdiction.
Courts Other tribunals.
Besides these federal courts, described as Article
Federal judiciary of the United States
The federal judiciary of the United States is one of the three branches of the federal government of the United States organized under the United States Constitution and laws of the federal government. Article III of the Constitution requires the establishment of a Supreme Court and permits the Congress to create other federal courts, and place limitations on their jurisdiction. Article III federal judges are appointed by the president with the consent of the Senate to serve until they resign, are impeached and convicted, retire, or die