How involved do Mr. and Mrs. Bennet seem to be in the upbringing of their daughters? At the ball where we first see Mr. Darcy, what is his...

There are a great many questions here; let's start with the one about Mr. and Mrs. Bennet. Mr. Bennet is a kind but not always tolerant man, who sometimes loses patience with people he deems to be foolish. He tolerates his wife's foolishness because he has grown used to it over the years. Mrs. Bennet is shallow and socially conscious. She wants her daughters to marry wealthy men and thus rise above their middle class upbringing. She is not above loudly gossiping about her daughters' availability or prospects at social gatherings.

Jane and Elizabeth are the most sensible of their five daughters. Jane is somewhat shy but Elizabeth is confident and outspoken; she is clearly her father's favorite and he takes her counsel in family matters. When Elizabeth is embarrassed by her mother's behavior, her father appeases her. When Elizabeth receives a marriage proposal and wishes to refuse it, her mother is appalled but her father thinks Elizabeth knows her own mind and should do what she thinks is best. Despite her penchant for gossip, Mrs. Bennet is very aware of the importance of reputation, despite not being a very good social role model for her daughters, and when young Lydia runs away with Mr. Wickham the resulting scandal weighs heavily on the family.

Mr. Darcy's first appearance at the ball draws the attention of many, especially the young ladies, for he is tall and handsome with a distinguished manner. But he is thought to be aloof and even rude, especially compared to his jovial friend Mr. Bingley. Mrs. Bennet seems to think the following of him: "He was the proudest, most disagreeable man in the world, and every body hoped that he would never come there again." Darcy only dances with two ladies and does not mingle; he also speaks unfavorably of Elizabeth and she overhears him say to Bingley that she is not pretty enough for him to want to dance with her. But his slight doesn't cause her any great distress: "She told the story however with great spirit among her friends; for she had a lively, playful disposition, which delighted in any thing ridiculous." It is not clear why Darcy behaves in this way, but we gradually learn that his brusque manner is somewhat rooted in slights and betrayals, including a difficult situation involving Mr. Wickham.

When Elizabeth says she could easily forgive Mr. Darcy's pride "if he had not mortified" her own, we see that she is a compassionate and reasonable person, and yet also possessed of enough of a sense of self-worth to not want to associate with anyone who disrespects her.