The story of Hamilton is based on real historical figures and events, but it does take some artistic liberties for the sake of entertainment and storytelling. For example, the dialogue and character interactions might be fictionalized to some extent.
No. Most Hamilton fanfics tend to focus on relationships like Hamilton and Burr, or Hamilton's love life with Eliza or Angelica. Themes of Hamilton 'watching' fanfic are not as common as the more traditional relationship - based or historical - exploration themes.
I really don't know the height of comic Ryan Hamilton. Sometimes this kind of information can be hard to come by. You could keep an eye on his social media or official biographies for any updates on his height.
Hogwarts could be incorporated by making it a place where the events of Hamilton's story are retold in a magical way. For instance, the duels in Hamilton could be turned into magical duels at Hogwarts. The Founding Fathers could be reimagined as wizards, with their political battles becoming battles of magic between different Hogwarts houses.
It depends on your perspective. Some parts of the Hamilton story are based on real events and people, but it also takes creative liberties for dramatic effect.
Hamilton is based on real historical figures and events, so it's not pure fiction. However, it does take some creative liberties for the sake of entertainment and storytelling.
Hamilton the musical is fictional. It weaves a narrative based on historical elements but adds elements of drama, music, and artistic interpretation to make it an engaging theatrical experience.