Mr. Rochester states in the book that he couldn't divorce her precisely because she was insane.
The implication might have been that his wife's family was richer and more influential than he was.
Insanity wasn't legal grounds for divorce, probably something to do with "in sickness and in health". There's an Agatha Christie novel written a hundred years later where one character still can't get a divorce because his wife is insane. Acts of Parliament were really not that easy to get passed. For starters, they were very expensive and, secondly, they were not really for the likes of people like Rochester, who might be gentry but sure as hell isn't an aristocrat. (Think of the difference in social status between Gilbert Markham and Arthur Huntingdon in The Tenant of Wildfell Hall.) Even then, there were a lot of aristocratic marriages in the period who basically agreed to live separately and have lovers, because getting a divorce was just that much of a problem, and that's before you even get into the stigma of it all.
Why didn't Jane go to Lowood or the Reeds' after her marriage failed? Both places would have let her stay long enough to advertise for a new job.
Because she was incredibly distressed and obviously not thinking straight? Because the Reeds' was a place of utter torment? Because Lowood might not be particularly welcoming to an ex-pupil who has left her place of employment under suspicious circumstances? Because she doesn't have an A to Z map, or any means of transport, and is a woman totally without friends and money, and therefore vulnerable and powerless?
"The Reeds' was a place of utter torment." As well, she mentions that after John Reed's death, Eliza went into a convent and Georgiana took up a high-living life, eventually marrying. If Jane had gone to Gateshead, there might not have been anyone there to help, even if they were inclined to.
The real reason is probably that Jane knew those would be the first places Rochester would look, and she wanted to escape him entirely.
Why doesn't Jane go to her former teacher and dear friend Miss Temple, now Mrs Nasmyth? They were close and they probably corresponded. Jane was carrying a letter to post after all when she met Mr Rochester. Surely Reverend's wife and her particular friend could offer her a room for some time and help to find her a new employment.
She's not exactly thinking straight, she ran away on impulse before thinking everything through, as such she set up a chain of events, by the time she got to a point where she could break the chain, she had already been offered residence and a job, so by that point there wouldn't be much point.
Why would Mr Rochester keep Bertha in the very same house where his ward and a bunch of servants live? He knows she's dangerous. He says he doesn't want her to get sick and die because of damp environment in his other house, but couldn't he keep her in a cottage house somewhere with just Mrs Pool? Madwoman in the Attic is the essence of Gothic novel and there is a Rule of Drama, but this is definitely a plot hole.
No one at Lowood shows any signs of having consumption other than Helen. TB is contagious and is spread by air. The school would be a prime environment for this to spread, but literally no one else gets it. If Helen hasn't left the school in a very long time, how would she have contracted it in the first place?
TB can be 'dormant' for years before a person actually begins showing symptoms. Keeping that in mind, who knows if she actually did pass it on to anyone else at the school, who just didn't figure it out until years later? The real question is how the hell Jane avoided it, since the two were often in such close contact with one another.