For one, the Chernow biography is not well regarded by many historians. It is incredibly biased in favor of Hamilton and against Jefferson. It's a good source for basic details on Hamilton's life but regarding other figures like Jefferson it comes close to full-on propaganda.

As regarding your specific questions: Jefferson, Hamilton, and Washington all engaged in petty partisanship and it was hardly limited to Jefferson. All of them were sponsoring newspapers and political diatribes against one another; they might've all claimed to be above it but things went quite differently than how they wanted. It's inaccurate to simply blame Jefferson for all of the 1790s' intense partisanship.

Regarding the French Revolution, it's hardly as clear cut as Chernow (who is not a historian) makes it out to be. I, for one, agree with Jefferson's position on it.

Annette Gordon-Reed has suggested the reason Jefferson kept running back to political office was likely because he felt that his service was needed for the country. He often expressed frustration with politics, as many politicians both then and now have, but he believed in ideas which were important to him so he felt that he needed to keep pushing for them even if it was stressful to him personally.

Now, I want to clarify that there is a very good reason why most scholars rank Jefferson in the top 5 presidents and American statesmen. I'll quote some of my comments from elsewhere on the same subject:

I think Thomas Jefferson was a better President than you give him credit for. He should get credit for the Louisiana Purchase as it required a lot of precarious diplomatic balancing between the interests of France, the US, Haiti, and Britain. The whole deal could easily have gone up in flames had it not been for Jefferson's skill with diplomacy.

Jefferson achieved other important goals as well; he defeated the Barbary Pirates which were preying on American shipping, and he achieved the abolition of the American slave trade. It's been popular among anti-Jefferson historians recently to portray the abolition of the slave trade as an easy achievement (and thus that Jefferson doesn't deserve much credit for it) but they ignore that the slave trade and support for it had actually been rising in the years leading up to Jefferson's presidency. Jefferson made a genuinely humanitarian and abolitionist gain here (indeed he was celebrated by contemporary abolitionists for it), and American warships joined Britain's Africa Squadron to try and put that terrible traffic down.

A lot of what Jefferson did was important in what he prevented from happening, rather than what he made happen. America was still a young nation at the time, and could easily have been heavily damaged from war. Jefferson was unique as one of the few politicians at the time who was an utter peacenik, making sure that peace reigned between America and Europe and also America and the Native Americans as well. You mention his Indian Removal proposal but contrary to Jackson's Jefferson would only have had those Native Americans who engaged in armed resistance moved. His Presidency was the last time period in American History where peace existed between the United States and the Native American tribes.

Jefferson is also important for two additional reasons, the first being religious freedom. He was the codifier of separation of church and state, and his Virginia Statute for Religious Freedom helped ensure that all Americans would have their religious freedom. The Statute includes "within the mantle of its protection, the Jew and the Gentile, the Christian and Mahometan, the Hindoo, and Infidel of every denomination." (Jefferson's Autobiography). This is in stark contrast to folks like John Jay and Alexander Hamilton, who advocated religious freedom for Christians only (something which Chernow completely glosses over in his book).

And of course, the other accomplishment I wanted to mention was the Declaration of Independence, which in its profound statements of human rights, equality, and revolution, has become a "stumbling block for would be despots" (to quote Abraham Lincoln). What Jefferson did here was immense, and his authorship of the Declaration would not only summarize the thoughts and hopes of a generation but also serve as a rallying call for reformers, radicals, revolutionaries, abolitionists, feminists, and socialists alike to fight for their rights and freedoms.

Obviously much of this is based on my opinion but Jefferson's accomplishments have been highly discussed and debated among scholars. Here are a few sources and potential further reading:

Most Blessed of the Patriarchs and The Hemingses of Monticello by Annette Gordon-Reed, along with much of her other work.

Thomas Jefferson by RB Bernstein.

Thomas Jefferson's Qur'an: Islam and the Founders by Denise Spellberg.

Ron Chernow’s Alexander Hamilton Is Not Throwing Away Its Second Shot

Edit: HOLY CRAP MY FIRST GOLD!! Thank you!