...a type of commitment in which the parents of a boy and agirl agreeon having them marry.
According to the information available on this excerpt, a betrothal is a promise which can be later modified, in which the parents of a boy and a girl promise to marry them. This could also be a definition of arranged marriage.
If they do things for them selves
Juliet, being a dynamic character, changes from being an innocent girl who does anything to please her parents to being a self-reliant girl who follows her gut and doesn't care about what others think about her decisions.
hope this helps!°ω°
I think it is talking about how the speaker feels about what is according during his life