Answer
each State was interpreting laws for itself.
The need for a national court system in the U.S. was due to the fact that each state was interpreting laws on its own. The Supreme Court of the United States was founded in 1789.
In the US federal court system, you may be referring to the US Court of Appeals Circuit Courts, which are sometimes called intermediate appellate courts because they are between the US District Court (trial court) and the Supreme Court of the United States (final appellate court).
false
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The US Supreme Court's ruling in the Marbury v. Madison case set the way in which the Court did not need to wait on the court system to bring a case before them and hear arguments. The Court was able to, and this remains to be true, that it can intervene on its own volition and decide on the constitutionality of government actions.
In the District of Columbia, legal cases are tried in the US District Court for the District of Columbia, which is part of the federal court system because Washington, DC, is federal territory, not a state. Similarly, each US Territory (e.g., US Virgin Islands, Guam, Northern Marianna Islands) has a territorial court that operates as a remote district court. Appeals of cases heard in territorial courts are filed with whichever US Court of Appeals Circuit Court has jurisdiction over that particular territory.
because states can govern themselves
You need to be more specific. Tell us when and where.
national court system, state court system and tribal court system.
(in the U.S.) that would be a reference to the Federal Court System (e.g.: US District Courts - US Courts of Appeal - The Supreme Court of the US - etc).
Yes, definitely. You do not need to be a US citizen to bring a lawsuit in the US court system.
Federal Court System
The US Supreme Court is the highest court in the US. Each state has its own Supreme Court, but the US Supreme Court is the end of the line.
The US Supreme Court is the center of the US justice system. The Supreme Court is the highest court in the country.
Federal Court System
Federal Court System
Federal Court System
Most cases reach the US Supreme Court via the US Court of Appeals Circuit Courts, which are part of the federal court system.