The formulas were part of the performance to allow the audience a moment to breathe while the singer could think about the next part of the story. These formulas for different aspects of culture such as greeting guests, eating meals, etc.
Answer:
Ponyboy picks up the glass because he feels bad about breaking it. It's strange considering his previous actions. This action is a relief to Two-Bit because it shows that Ponyboy isn't completely hardened.
I believe it would be person vs. person because she’ll probably have a conflict with her mother for not letting her go..?