Generally speaking, we can divide Act 3 into two parts. One part is in Mrs. Higgins' house where Elisa has a small talk with Mrs. Hill, Clara and Freddy. The other is the party at an Embassy.
In the first part, Higgins tells his mother everything about Eliza and what he is doing with her. He wants to take Mrs. Higgins' at-home day as his experiment day, to check if Eliza's English level can be presentable or not. At the beginning, although Eliza's action is a little bit unnatural or is mechanical like a robot, for example, she speaks 'How do you do' with a pedantic correctness of pronunciation and beautiful tone to people who attend the tea party and shakes hands stiffly with others (imagine how the movie presented). The situation still goes well. But the marry atmosphere turns to a embarrassing situation when Elisa mentions about her aunt's death. Everyone is shocked or stunned by such a dreadful topic and rude language for conversation, for in that age tea party should be elegant in high society. Fortunately, it is smart of Higgins to say ' Oh, that's the new small talk' to defuse this crisis. And I think what interesting in this part is the dialogue between Higgins and Clara, which is on P.66. It says that,
Higgins Goodbye. Be sure that you try on that small talk at the three at-homes. Don't
be nervous about it. Pitch it in strong.
Clara I will. Goodbye.
It keeps me laughing when I imagine this scene in my brain. I think Clara will deeply believe what Higgins says is true, and regards a small talk as a fashionable thing. In order to up to date, she will makes her efforts to follow the fashion, fit herself in the small talk. Mrs. Hill believes, too. She thinks the reason why Clara can't catch up the fashion is because they are poor genteels. She says,'' We're so poor! And she gets so few parties, poor child! She doesn't quite know. ''It's funny, but also irony, isn't it? Maybe Bernard Shaw tries to satirize something of the age he lived: the middle or upper class were only willing to do things those can satisfy their vanity or things in fashion. If they didn't do these things, they would feel so disgraced. What a strange attitude!
In P.70, Mrs. Higgins says,''No,ˇK: the problem of what is to be done with her afterwards.''
She is not such a egoist as her son, who only cares his own matters, so she can sees the problem beforehand. She thinks of Eliza as a human being, maybe that's why Eliza stays at her place after she leaves Higgins' house. This character has more compassion than her son.
The climax of this drama is when Eliza attend the party at the Embassy. She is so charming and attractive that she catches everyone's eye. Just like the sentences inP.74 says,''They stop talking to look at her, admiring her dress, her jewels, and her strangely attractive self. Some of the younger ones at the back stand on their chairs to see.'' Not only because Eliza changes in external ( like the way she dressing) , so she can be eye-catching, but also because she indeed has became mature and grown up in mental. After the education from Higgins and Pickering, she pronounces perfectly, also she has more her own thoughts about the values and becomes more confident of self-identity. For example, Nepommuck thinks Eliza is a foreigner, who were taught too speak like this, for she has too excellent pronunciation. And also the elegant temperament that she reveals makes him insists that she is a Hungarian princess.
As for the question about why Shaw writes ''ˇKshe walks like a somnambulist in a desert''. I guess maybe because it's the first for Eliza to experience such a formal occasion, being nervous is unavoidable. In addition, she is intent on her ordeal , so that she walks like a somnambulist in a desert.
In the party, they meet Nepommuck, who is one of Higgins' pupils. He knows 32 language. So he can easily knows other's class origin by analyzing his accent. He takes his knowledge as a to tool of earning money, so that he threatens others with this skill to get richer. I think he is a hypocrite, for he acts like a upper class in appearance, however, he does those illegal things in private which disobey the normality that upper class should have. What he says doesn't correspond to what he does.