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) 
Also ,the F.J  It is generally an appellate court that operates under discretionary review,
Yes. I call the Federal Judiciary the last resort for the people
Last resort rule
In Constitutional law, the Last Resort Rule is a largely prudential rule which gives a federal court the power to avoid a constitutional issue in some circumstances. This rule dictates that, even if all other jurisdictional and justiciability obstacles are surmounted, federal courts still must avoid a constitutional issue if there is any other ground upon which to render a final judgment. The last resort rule can function as a distinct barrier to Constitutional avoidance. It is articulated by Justice Brandeis in Ashwander v. Tennessee Valley Authority.
The
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