Bring on the tough stuff - there’s not just one right answer.
What purpose do you think the history of San Lorenzo Island serves in the novel? Does it help explain the motivations of certain characters? Does it progress the plot in any meaningful way? Does it enhance a certain theme?
Does Cat's Cradle contain any strong female characters? If yes, who and what make them strong characters? If no, then explain why not. Either way, why do you suppose the female characters are characterized the way they are? What purpose does it serve the novel thematically?
Do you think Felix Hoenikker is the antagonist of Cat's Cradle? If yes, why? If no, then who is the antagonist—is there one?—and why? Don't forget that there textual evidence.
Claire Minton briefly mentions that Peter Castle is a homosexual. Why do you suppose this tiny detail was added to the character? What purpose does it serve the novel? Does it advance characterization or heighten a certain theme?
That whole Krebbs scene was kind of random, wasn't it? Why do you suppose it's even there? Does it alter John's character or does it play toward a theme?
This one requires a little research. Find out what you can about the Manhattan Project and the Hiroshima atomic bomb. Do you think Cat's Cradle's treatment of the subject matter is fair? If yes, explain where the novel got things right. If no, then where did it go off track?
Time to play movie producer. Imagine you're producing an adaptation of Cat's Cradle. How would you go about it? This question can be answered from many different directions:
How would you film the novel's scenes such as the letter scenes and the scenes with John reading?
How would you plot the movie's progression? Would you leave scenes out? Switch the order?
Who would you cast for each role?
What themes of the novel would you bring to the forefront? What would you leave out?
What style of cinema would you go for? Modern? Black-and-white? Old-timey newsreel? A mixed bag approach?