When I'm looking for good essay questions for any novel, I always look first at the theme(s). Next, consider the literary elements, such as characters, irony, symbolism, etc.
For example, one theme of this book is appearance vs. reality. One questions might be: "Explain how the characters in Ten Little Indians deceive each other about their true natures." As for the theme of justice and injustice, you might ask, "Explain and give examples of how justice is served and when injustice occurs."
Literary elements always provide a wealth of information for questions, such as compare and contrast characters, discuss the irony and symbolism, etc. Conflict(s) is/are always a good source to consider for essay questions. "Describe the conflict (one of characters) must deal with in the book, how he/she resolves it, and what this says about that character."