The Pax Romana happened under Augustus' rule.
Exclusive jurisdiction is when only a single court, or a type of court, has jurisdiction over the matter in question. An easy example for this is that the United States District Courts have exclusive jurisdiction in cases of bankruptcy, or that the Supreme Court has exclusive jurisdiction on reviewing other courts' decisions.
He was an Anti-Federalist. He did not believe in the Constitution's ratification because he believed the government would gain too much power, and individual rights would not be granted.