This fascinating novel clearly concerns the theme of slavery and our relationship with it, both today and in the past. There are a number of sections of the novel where characters realise that the wall protecting them and separating them from the radically different world of slavery in their own country just a few years ago is actually very porous. This should lead us to really think about and consider what the impact of slavery and the kind of violence, segregation and complete power that whites over blacks have in this story impacts us today. Through the motif of time travel the author allows two very different worlds to collide, and this collision changes Dana permanently forever. How does the novel change us?
Secondly, you might like to think about some of the choices Dana makes to ensure her own survival, both in the past and then through trying to ensure her survival in the future, as a descendant of the characters that she meets. Was she right to persuade Alice to sleep with Rufus so that she wouldn't be beaten again? Should she have tried to teach some of the slaves to read? An important aspect of this story is the way in which the author suggests a different moral code was in order from the Christian idea of ethics. In such a world of slavery where you are deprived of every right, is it morally acceptable to sleep with your white master to avoid torture and pain? Such issues force us to evaluate our own morals and ethics and to consider how context-specific they are.
These are some issues and questions that should get you started. I have provided some links below that should also help. Good luck!