1. Novel, set in: The Leopard, by Giuseppe di Lampedusa.
2. Movie, set in: This is a tough one. But I'll opt for Visconti's The Leopard (big screen required, don't bother with Netflix) over Coppola's Godfather sequence, not to mention La Terra Trema and L'avventura. Wow. Is there a Sicily scene in Patton?
3. Chess opening: 5…a6, the Najdorf. Chess is a good example of the more general point that it takes a long time to discover which innovations turn out to be valuable and which not. Thirty years ago, who would have thought that 6.Be3 would become the most common response?
4. Playwright: Luigi Pirandello, but I would call this a "favorite only because I can't think of anyone else."
5. Opera composer: Bellini, especially the first Act of Norma, sung by Maria Callas. There is also Alessandro Scarlatti but I don't know his music well.
6. Musical arranger: Pete Rugulo, yes he was born in Sicily and later he arranged for Stan Kenton. That music still sounds impressive to me.
7. Philosopher: Gorgias was smart but cynical (if we trust Plato). Empedocles was sooner a natural scientist in my view. Archimedes I would count as a mathematician.
9. Movie director: Frank Capra was born in Sicily; see my comments on Pirandello. Note by the way that I am not considering Sicilian-Americans unless they were born in Sicily.
They have a bunch of accomplished writers and poets I'm not familiar with, other than Lampedusa, so I don't have a favorite there.
The bottom line: A nice, diverse list, with numerous surprises.