There is a very significant difference between Elizabeth and her mother, though, as Lydia is their mother's favorite, there are a great many similarities between Lydia and their mother. As we are limited in space to discuss all the points you mentioned, here are a few points concerning attitudes and actions to help get you started.
Elizabeth has a great deal more sense than their mother does and acts more sensibly and with propriety. In fact, Mr. Bennet feels that Elizabeth and Jane are the only two women with any sense in the entire household. Plus, between Jane and Elizabeth, Mr. Bennet thinks that Elizabeth "has something more of quickness than her sisters," meaning intelligence, making her his favorite. All of the other sisters, including Lydia, he describes as "silly and ignorant" (Ch. 1).
Lydia, in contrast, is just like their mother. She has absolutely no sense of either decorum or propriety. Lydia is also described by the narrator as being incapable of listening to either Jane's or Elizabeth's advice because they she is too stubborn and too inclined to pursue her own interests. She is also described as being "careless ... ignorant, idle, and vain" (Ch. 37). At the time that the Forsters invite Lydia to go to Brighton with them, Elizabeth even warns her father that if he does not start controlling Lydia soon, "she will, at sixteen, be the most determined flirt that ever made herself and her family ridiculous" (Ch. 41). In other words, Lydia is in danger of ruining her own and her family's reputation through her improper behavior, particularly her flirtations with every officer she encounters. We see the similarities between Lydia and their mother when the narrator describes Mrs. Bennet as having a "weak understanding," in other words, as being ignorant, and as having an "illiberal mind," meaning being "selfish" (Ch. 42; "Liberal," Pemberley.com). We also especially see Lydia's similarities to their mother when Mrs. Bennet behaves with impropriety at the Netherfield ball, such as announcing in Bingley's own home, loud enough for him to hear, that Jane will soon be engaged to Mr. Bingley well before Bingley has actually proposed.