Connection between Izzy's feelings and fer first quotation is Option 4: "Just like Juliet, Izzy's goals are at odds with her parents' plans".
Explanation:
William's Shakespeare's "Romeo and Juliet" is a doomed story about two young lovers who are from the feuding families. Juliet fell in love with Romeo while her parents Capulet and Lady Capulet wanted her to marry Paris. Thus, they had different plans for Juliet.
For Izzy, this world is stage where she wanted to act. `When she says the lines where she asks her father to be patient and listen to her, the connection between her and her first quotation is that her father also has different plans from him than what she thinks.
"Has" is the correct answer. This is because your friend is the subject here and you don't need to include "along with her sisters". "Your friend" is the subject and a singular subject is a singular verb...