A thematically oriented question that may get a conversation revved up would be "In what way(s) is each character corrupt?" Or, "Can we rank the characters in The Great Gatsby from least corrupt to most corrupt?"
Moral corruption and duplicity are themes in the novel. Yet, as much as they are clearly presented, they refuse to be simplified into a single type or category. Students may be interested to talk about how there are various modes of corruption at work and various levels of corruption as well.
You might ask them how they think the U. S. has changed (and/or remained the same) since the 1920s, especially in attitudes toward wealth and in the roles of women. Is Tom Buchanan the kind of character who now seems an anachronism, or are there still people like Tom Buchanan walking around today? In general, do they think the book seems dated? Is it valuable mainly as an historical (and aesthetic) document, or is it still relevant to the ways people live today? Of course, the answers to these questions may be mixed (with some aspects of the book seeming dated and others still seeming relevant).
You have a wide array from which to choose. If your class is able to understand the history, I think that a good question to ask would be how the work reflects the time period. What is Fitzgerald saying about the 1920s, in general? What is Fitzgerald suggesting about conformity and being a part of the social elite? I think that this could spawn into a very interesting discussion about how he shows personal cruelty. I think that a very good discussion point in the novel is the different levels of cruelty that is evident. As readers, it is important to find examples of this cruelty to see if it is replicated in our own lives or if we have learned anything from it. Another question that should reveal some interesting discussion would be how Fitzgerald defines love. Is there any character in the novel that really "loves" another? If so, what does it mean to love? Is there a difference between "love" and the idea of "being in love?" I think that this might be interesting to assess in a class forum. Finally, I think there should be a discussion about the American Dream. What does it mean? How close does Fitzgerald link the American Dream to the American Nightmare? I think that this might be a very interesting point of discussion.
I would start from the students' experiences. Have they ever tried very, very hard to impress someone? How would they relate impressing others to the relations in TGG? Have they ever idolized someone? How would they relate idolization (or idealization) to TGG? Do they believe that the US is exceptional in some way (or ways)? How does that exceptionalism manifest itself? In TGG? Do they think some people are evil? How does evil manifest itself? Etc. Good luck.