Dear LW1: Your mother has obviously taken for her role model that anti-paragon of parenthood, Mrs Bennet. We are told frequently that it takes a great effort on the part of Mr Bennet to be able to keep the household expenditure down to a level that is just barely within his income. I recall reading a spot-on critique once of Mrs Bennet in which her attitude towards Jane's beauty was called that of a procurateuse - the fond mamma viewed her eldest daughter not as someone possessing a sweet and virtuous character but more as a piece of stock that could fetch four or five thousand a year on the marriage market.
In part, how to handle this feels like a technical question. One wants to call foul on the Prudecutor (well, one wants to do that anyway, if one must be completely honest, about seventeen times every week) for inserting a question that is so much about various legal steps to take. Surely this sort of question ought to be sent to someone more specialized. But it does allow the Prudecutor completely to duck the question of the ongoing relationship with M1. Thankfully, LW1, you have the potential example of an assortment of daughters. Jane would respond that of course it was very wrong of her mother to act so, but would forgive her and probably pay off more of her mother's debts. Elizabeth would have less patience and would probably take appropriate legal steps to restrain her mother's conduct. Mary would spout platitudes about identity theft and then, on a good day, realize that she had no clue what to do about it. Kitty would have a coughing fit. Lydia would adopt her mother's tactic.
So there you are, LW1 - five separate courses of action. Pick your favourite Miss Bennet, and your dilemma is solved.
Dear LW2: Do you admire Miss Woodhouse?
This letter has Emma written all over it. Sarah's genetic disposition could be a complete rewrite of the question of the Dubious Parentage of Harriet Smith. We all recall how Harriet is the Natural Daughter of Somebody. Harriet herself is content with not being able to know her father; Emma, almost immediately after befriending Harriet, is quite sure that, in such a position, she herself would have been both unwilling to settle for such ignorance and successful in discovering her true origins. At least in one respect, LW2, you have the advantage over Emma in that her elaborate suppositions leading to her eventual confidence in Harriet's father being a gentleman are entirely the product of her own fancy, whereas you at least have done research into facts, rather as Mr Knightley might have done.
The story then takes a turn into one of the few chapters in the book in which Emma does not appear - the conversation between Mr Knightley and Mrs Weston during the course of which Mrs Weston advises that it would be unwise for Mr Knightley to follow his inclination to canvass John and Isabella for their opinions during their upcoming holiday visit. You and Mr Knightley both yielded.
I would place where the story is now at about the point at which Emma and Mr Knightley have a major difference of opinion. Emma dominates Harriet into refusing the marriage proposal of Robert Martin, shortly after Mr Knightley heard out Robert's plans and advised him that he was proceeding in a sound manner.
Therein lies your choice, LW2. You doubtless know how your friend will react to various possibilities. You can be Emma, or you can be Mr Knightley. The choice is yours.
Dear LW3: The Austenian component is a bit thin here. It would certainly be possible to go back to Pride and Prejudice and think of Mr Collins assiduously courting the patronage of Lady Catherine de Bourgh, but I shall move on to Persuasion, where this can be framed as a tricky comparison to the relationship between Sir Walter Elliot and Mrs Clay, especially as the Prudecutor seems to be presuming to side with or feel like Anne Elliot in opining that LW3's male colleagues are jockeying to see exactly which of them gets to be her Sir Walter.
But this leads me directly to a feminist thread of mentoring that I read from a while back. LW3, you have the idea of a mentor in the back of your mind, but the concept completely sails right over the head of the Prudecutor. Indeed, her attitude is exactly the sort of claptrap that is preventing the expansion of mentoring into the model needed to assist the advancement of women in many fields. The question the Prudecutor completely fails to ask is whether this is how the men are mentoring other men. A personal response would be that one has no idea, but it seems plausible enough. Now one might expand in due course into what necessary differences there may be for cross-gender mentoring, but it would be a bit disappointing for this all to devolve into men, on being told that they must mentor women, as they've been mentoring men, attempting to do exactly that, only to be told that they're Doing It Wrong.
On the other hand, given this particular situation, your instinct is not to be comfortable with the invitations you've been issued. There ought to be some way to work your way into mentoring situations that is as comfortable to you as the current system is to the younger men these elders mentor. The Prudecutor's road doesn't go there.
Dear LW4: While I can hear Mrs Elton proclaim that their coachman and horses are so extremely expeditious, and that she believes they drive faster than anybody, I'll pop over to Northanger Abbey instead. Although John and Isabella Thorpe are brother and sister instead of husband and wife, they fit neatly into the same sort of blustery exaggeration as that perpetrated by your friends. Happily, I doubt that they are slated to remain friends much longer.
Moral: "It is very good advice, and it shall have a better fate than your advice has often found; for it shall be attended to."