Per Wikipedia, Michaelmas term tends to around in mid-December, not in mid-November.

Well then I guess it was an unseasonably warm December that year? Or perhaps the dates have changed? Regardless, I'm not at all convinced that it makes a significant difference to the story.

It’s a helpful detail that Dickens wrote for his Victorian readers. Michaelmas term refers to both the first academic term of the school year and the start of the legal year in the English courts system. Bleak House is about a court case that has gone on so long that nobody knows what it’s about. The case is about an inheritance and has dragged on for so long that the estate itself has been totally wiped out by legal fees. It has ruined lives and continues to ruin them but there is no end in sight even though there’s nothing left but fighting to fight over. It’s an inherited lawsuit and an inherited feud.

Dickens had a lot of issues with the legal system at the time and it was a protest work.

> nothing left but fighting to fight over

Toward the end of the story the fighting does stop when lawyer's fees, which they had been charging to the estate, at last empty it. This is announced publicly in court, and the attorneys respond by flinging their piles of paper into the air, one of a few comic scenes in the novel.

FYA, this modus vivendi is still being practiced -- see the litigation around the estate of O.J. Simpson.

How does November help? I don't even remember the academic terms from my college 10 years ago, how am I supposed to accurately know how academic terms worked a century ago in England?

One example student in the study does not look it up and misinterprets "Michaelmas Term" as a person, presumably because it has "Michael" in it. Knowing it is even a time is half the battle.