The Judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;—to all Cases affecting Ambassadors, other public Ministers and Consuls;—to all Cases of admiralty and maritime Jurisdiction;—to Controversies to which the United States shall be a Party;—to Controversies between two or more States;—between a State and Citizens of another State;—between Citizens of different States,—between Citizens of the same State claiming Lands under Grants of different States, and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects.
It is the Judiciary’s responsibility to interpret the Constitution and all laws passed by Congress. It will also interpret treaties made with other nations. When there are disputes between states, people who reside in different states, or any disagreements between states and the Federal government, it shall be the responsibility of the Judicial branch to handle that.
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be a Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the Supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
So, when some official from another country is here and has something happen that needs the Law to sort it out, the Supreme Court is the original jurisdiction. Otherwise, any Federal case will start in the local Federal court and will only go to the Supreme Court if there is an appeal. Congress has the power to make changes to this in law.
The Trial of all Crimes, except in Cases of Impeachment, shall be by Jury; and such Trial shall be held in the State where the said Crimes shall have been committed; but when not committed within any State, the Trial shall be at such Place or Places as the Congress may by Law have directed.
All criminal trials in Federal cases will be by jury and in the jurisdiction in which the crime was said to have been committed. If a crime was not committed within a state (such as in a US territory), Congress can say where the trial shall be held.