Hello, this is a great question.
The issue of responsibility is explored in the relationships between the characters in the story. Who is responsible for whom in this story? How about Lily and Rosaleen? How does Lily show she is responsible for Rosaleen? How does the story show how Rosaleen is responsible for Lily? What about August and her responsibilities for her sisters or for Lily and Rosaleen? Did Deborah fulfill her responsibilities to her family? Why or why not? Were the sisters of Mary responsible for one another? You could probably pick any two characters in the book to discuss the issue of responsibility.
On a larger scale, there is the idea that white people might have some responsibility for what had been done to African-American people in the past. Do any of the African-Americans in the story have any responibility for their behavior toward white people? What is June's response to Lily?
The issue of forgiveness is important in the book in many ways. You might notice that no one in the story can really heal or move on until he or she forgives. As with responsibility, you can pair many sets of characters and discuss forgiveness. Lily and her mother are one example. Who does June have to forgive before she can marry Neil? Does Rosaleen carry some resentments? T. Ray is someone who may not have forgiven his wife, and this prevents him from being a fully realized human being.
As you can see, these are important themes in this story, and if you can think about just a few of the questions I have posed, you will be off to a good start.