Bring on the tough stuff - there’s not just one right answer.
If Myshkin is a Christ figure, then what are we supposed to make of the fact that he doesn't really save anyone at the end of the novel? Or does he save someone? Does this make the novel a tragedy or a satire? Why?
If the novel were set today, which parts of the plot would stay the same? Which would have to change? Which characters could you imagine just needing to change from Victorian clothes into jeans? Which ones would need far greater alterations? Why?
How would the novel be different if it were written in first person instead of third person? Whose point of view would be interesting to read? Nastasya's? Mrs. Epanchin's? Ganya's? Would it be better to read it from the point of view of someone likable or one of the less pleasant characters?
Are there misunderstandings you can predict if one character were forced to figure out the motivations behind the actions of another? Who would have the most trouble understanding whom?
One of the most Jesus-like things Myshkin does is constantly, and inappropriately, speaking in quasi-parables. Think about the story about hearing the donkey bray, or the long tale of the man condemned to be executed, or the story about the old guy who helps prisoners in a labor camp. Compare this to the New Testament parables about the good Samaritan or the prodigal son, for example.
Take a look at some of Myshkin's parables. Do they have a moral point? Do they tend to have a connection to the situation at hand, or the person hearing them? Why does Myshkin tell these stories?
Ok. You're the hot shot behind this novel's marketing, and you're thinking of the future. Which character or which plot thread could get its own spin-off? Whom do we want to hear more about? Who would do best in a spin-off novel? TV show? Which characters could least pull it off?
Compare the novel's parents and parent stand-ins. What are the similarities between the two intact families we see—the Epanchins and the Ivolgins? What are the differences? How do the parents influence the kids? What are the similarities and differences between Totsky, a kind of father figure to Nastasya, and Pavlichev, Myshkin's benefactor? How did each involve himself in the life of his ward? To what effect?
If you think about it, Myshkin isn't the only truth-telling character in the novel. Nastasya also has a streak of speaking the truth (like when she tells off Totsky, for example), Ippolit gets to spout his thoughts about what's what in his confession, and several characters try out their versions of the truth during that game at Nastasya's birthday party. Can you compare two truth-tellers to each other?
How does Nastasya's style of provocation compare with Ferdyshenko's, for example? What is the difference between the way Msyhkin says unpleasant things to people (telling Mrs. Epanchin that she is a child, for instance) and Ippolit's way of doing it (like calling Ganya out for being a leech)?
How would you have arranged the romantic pairings? Who should have gotten together with whom to maximize happiness? To maximize romance? Are there people who just should have stayed alone and unmatched?