In the election of 1800, Jefferson felt that he was turning the country away from militarism and monarchy, even though Adams had already taken care of any chance of militarism, and there was never any real threat of monarchy. James Madison, who later was involved in the forming of the Constitution, became Jefferson's Secretary of State. William Marbury, famous for the Marbury vs. Madison case, was one of the "midnight judges" Adams appointed before the end of his presidency. The chief justice of the Supreme Court, Marshall, concluded that there was no way for Marbury to get his commission from Madison; the question of whether the Supreme Court had the power to declare a law of the land unconstitutional came about. The historical significance of the case is the fact that the Court can overrule the President and Congress by a majority vote, and there are few other nations in the world where the courts have held such high powers.
Impressment was when Britain began seizing American ships and making sailors whom they claimed to be British subjects serve in the British navy. America then ceased trade with Britain, hoping it would help end this impressment. When that didn't work, they sent a man named Jay over to Britain to try to make a compromise with the British. However, the British knew the United States weren't going to do anything if they didn't agree to our terms, so they didn't feel the need to comply. The only thing Jay's Treaty really accomplished was the fact that Britain agreed to leave the frontier fur posts in American territory and they opened India and the West Indies to American trading vessels. The War of 1812 ties into impressmet and Jay's Treaty, because America once again ceased trade with Great Britain, as it did during the times of impressment.
Napoleon had a plan to create a new French empire in America, and he believed he needed control of the island of Haiti to be able to accomplish that. The French only owned the small western end of the island, and 500,000 of the 600,000 people living on the island were slaves. The slaves revolted during the French Revolution and killed the white people. Slavery was abolished, and Pierre Dominique Toussaint L'Ouverture became commander in chief of the armies on the island. America knew they wouldn't be able to continue expanding if Napoleon did manage to create his French empire in America, so they were relying on what happened in Haiti to determine the fate of the United States.