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 
The F.J has the , the Last Resort Rule is a largely prudential rule which gives a federal court the power
It gives the court power to overrule decisions that won't be  good to the people of the United States
Well they can go to supreme court which is  the highest court within the hierarchy of courts in many legal jurisdictions.
Yes but the problem is when the supreme courts judges are appointed by the president, the courts looses their independence to a certain level
Precedent
In common law legal systems, precedent is a principle or rule established in a previous legal case that is either binding on or persuasive for a court or other tribunal when deciding subsequent cases with similar issues or facts. Common-law legal systems place great value on deciding cases according to consistent principled rules, so that similar facts will yield similar and predictable outcomes, and observance of precedent is the mechanism by which that goal is attained. The principle by which judges are bound to precedents is known as stare decisis (
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