Yes, very much so. In 1807 Napoleon as very strong and the British were struggling in Iberia. In 1812, Napoleon was invading deep into Russia and the British were doing well in Spain.
Not sure yet, I'll have to look it up.
Hamilton's relationship iwithbBurr is complicated and various sources have recorded various things. But one thing that is certain is that after years of friendship Burr and Hamilton's relationship deteriorated into bitterness. It possibly started when Burr was sly about the Manhattan Water Company and tricked Hamilton and continued when Burr defeated Hamilton's father in law. This bitterness was exacerbated by their differing political ideals and ambitions. During and after The 1800 election Hamilton spread vitriol about Burr. Meanwhile for Burr and Hamilton's duel the site selected was the site of the pace where Hamilton's son was killed in a duel.
The conspiracy is most probably a hoax. The witnesses of it were a few unrealiable people. And the reason it became such a big thing was because Jefferson wanted to ruin Burr. There is no actual evidence of the conspiracy neither now nor then. Which is why Burr was acquitted of the crime. A lot of Burr's bad rap comes from how Hamilton, Jefferson, and their allies smeared his name.