Burr and Hamilton had a dispute over politics. Burr was running for president and Hamilton said some things that ruined Burr's chance at president. Burr and Hamilton decided to duel out their conflict. Hamilton shot behind a tree and Burr shot Hamilton right between his ribs. This resulted in Hamilton's death. Listen to The "Election of 1800" and "My Obedient Servent" of the Hamilton soundtrack on YouTube. It might be helpful.
The major charges against Anne Hutchinson are that she spoke up against the Puritan religion of the settlers which was a very strict Christian society. Hutchinson believed strongly in something different than what was taught to them an, therefore, she held meetings with other town people and wrote petitions against the Puritan church’s teachings. She believed in Antinomianism “anti” (against) “nomos” (laws) where Puritans are exempt from obligations of moral law
Hutchinson was aware the church teachings were wrong and consequently attempted to expose their lies to the innocent people who followed the religion. Hutchinson threatened the power of the church, priest, and ultimately, to them, God but the fact that Hutchinson was a woman defying the head power made the situation worse.