What is the theme of Lady Windermere's fan?
Enotes users are only allowed one question at a time, so I edited your question to the gist of it, and will answer the most important one which is about the theme of Lady Windermere's fan.
The play is about Lady Windermere, a young woman whose impeccable character makes her the proper example of the pruddishness that was rampant in the times of Oscar Wilde.
This woman receives the news that her husband has been visiting a woman, a Mrs. Erlynne, who has come to London to be taken back into society. Lady Windermere also finds out (through the Duchess of Berwick) that her husband has spent countless amounts of money on Mrs. Erlynne to help her "settle in."
As she confronts her husband, she still does not get a definite answer as to why he is taking care of this woman. She also does not understand why she is now obligated by her husband to not only accept her in her house as a guest for her birthday party, but that she also must extend an invitation to other visits. This would make those do not know Mrs. Erlynne acceptable in the fashionable set of the London upper classes.
Slowly we realize that the money that Lord Windermere has been giving this woman was under a form of blackmail, because the woman's main interest is to marry well, perhaps even with a Duke, or someone of title for marriage.
Once she marries into the ranks, she will be able to reveal the truth. She is the real mother of Lady Windermere. Her shame at her lack of rank, title, money, and class would have never allowed her near her daughter.
However, Mrs. Elynne chooses the wrong way to convey her need. She uses blackmail, lying, and deception, regardless of whether her actions will mend ties with her daughter or not.
Therefore, the theme of the novel is deception versus goodwill. When Lady Windermere believes her husband is cheating on her with Mrs. Erlynne (which was not true), she becomes Lord Darlington's lover as a way to get back at her husband.
Again, deception (self-deception in this case) is used for the sake of making up for lost love. Yet, the story shows that, in the end, deception will lead nowhere. The past and present of each individual is an individual's own making and creation. Mrs Erlynne eventually has to leave again, but does so without confessing her secret. Lady Windermere is caught within the fire of jealousy and Mrs Erlynne's defending her from committing adultrywith Lord Darlington.
The fan is what unites them, since it could have been proof of deception from Lady Windermere and Lord Windermere. Once Mrs. Erlynne takes the blame for the fan which is left "by accident" at Lord Darlington's house, her reputation goes back to being bad. She has to live with deception once more, a deception of which she is not guilty. Likewise, the Windermeres continue to pretend that deception never takes place, and pretend to go on with life as usual, deceiving themselves and absorbing the huge blow that their marriage takes.
Hence, deception versus good will shows that what begins in chaos, ends in chaos.