I have had to edit your question as you originally asked more than one and also your question was not too clear. I have chosen out of the list of topics you gave to focus on the emotional effect of this great story.
Clearly, this story concerns a conflict between a mother and a daughter. What makes this conflict more interesting or perhaps more divisive is the fact that both characters have very different outlooks on the world. Jing-Mei's mother is a Chinese immigrant to the United States, who has massive hopes for her daughter, wanting her to be a "prodigy". Jing-Mei comes to resent the pressure and the expectations her mother places on her, and as a second-generation Chinese immigrant she is born in the United States and thus has a very different outlook on life.
The conflict that occurs between these two characters reaches its climax after Jing-Mei's ludicrous piano performance when she brings shame upon herself and her family. Jing-Mei's mother's insistence that she continues to practice brings about the most heated and emotionally intense argument they have had:
"Too late to change this," said my mother shrilly. And I could sense her anger rising to its breaking point. I wanted to see it spill over. And that's when I remembered the babies she had lost in China, the ones we never talked about. "Then I wish I'd never been born!" I shouted. "I wish I were dead! Like them."
Clearly this is a key part where Tan uses the insults and the conflict between the daughter and the mother to contribute to the emotional effect, as in their anger, both say things that are incredibly hurtful to the other and words that will not be forgotten.