The major conflicts that develop in the range of chapters that you are asking about have to do with the relationships of Jane and Elizabeth Bennett.
Elizabeth receives a proposal of marriage from Mr. Colllins, a proposal that she adamdantly will not accept no matter how it will help her family to keep their home in the future.
Elizabeth rejects Mr. Collins, her cousin, who is a silly man, but then feels a sense of remorse about allowing a proposal of marriage to get away.
Jane, who has fallen in love with Charles Bingley and believes that he cares equally about her, is shocked to discover that the Bingley party has left Netherfield in a great hurry.
Jane is left to wonder why Charles and his party left for London. This creates a conflict for Jane who does not understand why her romance with Charles did not work out.
Jane goes to London with her Aunt and Uncle only to be ignored by the Bingleys which deepens her feelings of rejection.
Elizabeth, back home, goes to visit Charlotte Lucas who is now Mrs. Collins and encounters Mr. Darcy and Lady Catherine DeBourgh. Her visit to the Collins creates a new conflict for her because Darcy hastily proposes marriage to Lizzie, a proposal that she refuses, shocking Darcy.
Elizabeth will not accept Darcy because she believes him to be an arrogant, superior, pompous individual without a heart. She has learned that he advised Charles Bingley that he though Jane did not care for him and that is the reason that he left the country so quickly. Elizabeth is furious at Darcy, creating a conflict between the two, Darcy is in love with her.
Towards the end of the novel, a new and serious conflict is created by Lydia who runs away with Mr. Wickham. This conflict, a scandal that can ruin the family name, is very serious and involves Mr. Bennet, Uncle Gardiner and eventually Mr. Darcy.
Resolving this conflict is very important to the plot of the novel. It is through Darcy's efforts to save her family that Elizabeth realizes that she was wrong about him. She comes to understand that she really does love him, which creates another conflict, because she has refused his proposal and does not know if she will ever see him again.
Darcy's actions on behalf of Lydia and the Bennet family are very important in bringing a resolution to the above conflicts. But Elizabeth has one more conflict to deal with in the person of Lady Catherine Debourgh who confronts her about the rumor that she heard that Elizabeth was engaged to her nephew, Mr. Darcy.
It is through this conflict that Darcy becomes aware of the fact that Elizabeth might still be interested in him, which leads to Darcy coming back to the country to ask Elizabeth to marry him and to Jane and Charles Bingley being reunited as well.