Jane is very good natured and strongly inclined to believe good about people. She finds it hard to believe that Darcy could have cheated Wickham out of an inheritance, so she does not know what to believe.
Mr. Darcy believes it is his fault for the elopement because he knew what sort of man Mr. Wickham was, and he had to much pride to let the world know. If he had exposed Mr. Wickham's character, then the elopement would not have taken place.
No, Jane and Elizabeth did not send Lydia money after she married Wickham. It was Mr. Darcy who provided financial assistance to ensure Lydia and Wickham's marriage could take place and to settle their debts.
Mr. Gardiner sends a note to Mr. Bennet saying that Lydia and Wickham have been found. They are not married, and they (or perhaps just Wickham) have not intention of being married, but they will marry if Mr. Bennet provides them with a hundred pounds per year, while he lives, and sees to it Lydia gets her share of the 5000 pounds left Mrs Bennet and the daughters when he dies.
I would not say she was a foil to these young women. Georgiana provides Darcy with a way of reasoning dispassionately about Lydia's elopement. The fact that Georgiana had nearly eloped with Wickham made it possible for Darcy to see that Lydia's eloping was something that could just as easily have happened in his own family. Also, the fact that Georgiana had nearly run off with Wickham made him feel guilty about failing to warn the Bennets.
Elizabeth says her love for Darcy appeared so gradually, she cannot really say when it began. She jokes that it started when she saw Pemberly, implying that she fell in love when she could see with her own eyes how rich he was, but Jane, to whom she is talking, laughs at this and asks her to be serious.
The heroine in Jane Austen's Pride and Prejudice is Elizabeth Bennet. She is a strong-willed and independent woman who challenges societal norms and ultimately finds love and happiness with Mr. Darcy.
Mr. Darcy is a gentleman. He has no occupation. He is wealthy because he owns a great estate, described as being ten miles around, which would mean possibly 3000 or 4000 acres. On this estate are farms and villages, which he owns, and the tenants pay rent or provide products of their labor in lieu of rent. He could have had an occupation, had he decided to do so. His cousin, Col. Fitzwilliam, went into the military, which Darcy could have done. And there were a few men wealthier than Darcy who went into the church. But it was unnecessary for him to do any of these things. He did have matters of business, which he attended to, and though we know Wickham's father managed Darcy's estate for Darcy's father, we have no indication that there was a steward or manager for Darcy, so it is possible he did this himself.
Wickham's excuse was initially that he had to go to town on business, and then he says he did not go to the ball because, in his words, "I had better not meet Mr. Darcy; that to be in the same room, the same party with him for so many hours together, might be more than I could bear, and that scenes might arise unpleasant to more than myself."
Brizana told Darcy that she wasn't worried about Duane and that she could handle him. She thanked Darcy for the warning but said she didn't need any help.
Mr Darcy noticed that Mr. Bingley was in love with her, but he did not want him to marry her because her family is not rich, and have no connections. He also claims that part of it was because he thought Jane did not show admiration for Mr. Bingley, and assumed she did not have feelings for him.
Georgiana did not elope with Wickham. She intended to elope, but her plans were discovered accidentally before she could do it. Her reason for wanting to elope was that she loved him and clearly was talked into deciding to do it by Wickham, possibly with a little help from Mrs. Younge.
It is clear that Wickham is a fortune hunter, a man who is out to marry a wealthy woman for her money. In fact Wickham needs money badly just to cover his debts. Lydia has no money, but Wickham is marrying her. Clearly someone is providing Wickham with money, and Mr. Gardiner is the logical person to do so. At that time, the Napoleonic Wars were under way. A quarter to a third of all the young men in England were going off to war, and a large number of them would never return. Women from good families could not get jobs except as governesses. If they did not have money, they had to marry well or become dependant or impoverished. There was a lot of competition for husbands. Wickham had nearly got away with marrying Georgiana Darcy and getting her 30,000 pounds. He had also nearly married Mary King with her 10,000 pounds. If he kept his act up, running away from his debts, he was very likely to find a wife with a similar amount of money, so a marriage to Lydia required such an amount. Mr. Bennet knew that Mr. Gardiner had a family interest in seeing Lydia married and further scandal prevented. He also knew that Mr. Gardiner had a lot of money. He had no idea that Darcy would have any reason to provide for Lydia.