Hello, this is Xuanrui Li. I really love this film and have watched it for several times. I think this movie is not a typical animation which is for kids. Instead, this is an animation for adults, and there are some things you can take out from the film. Here are my answers to the prompts:
First, as for the bathhouse, I feel like it is the innocence and purity within people's heart. Human's society is really complex full, and people intrigue against each other. Such complexity can stain people's soul. The bathhouse is the place where people can find the purity again. That is also why all the people working in the bathhouse can smell Chihiro and think she is stinky. Therefore, the spirits in the bathhouse are the representation of people's pure souls.
Haku supposes to be the henchman of Yubaba, but he helps Chihiro a lot, because he feels he knows Chihiro but can not remember exactly, so he was curious about this. Also, his name was also taken away by Yubaba, so he is sympathetic to Chihiro. Finally, Habu loves Chihiro.
By the end of the story, she becomes more independent and strong. She also knows how to deal with different situations and how to get along with different people. Through the experience she works in the bathhouse, she becomes much maturer.