This one may seem like a stumper but in fact it's a breeze. Here goes:
1. Painter: Canute Calliste, who paints in a naive style. You'll find four images and a bit of biography here. I first encountered his work at a Quito biennial in the mid-1990s. His best works are not on-line. Here is one other painting by Canute Caliste.
2. Short story writer: Paul Keens-Douglas. This pick is a no-brainer. Here is Keens-Douglas telling a story. Here is Keens-Douglas doing a comedy routine. I used to have some very good cassettes of him telling folk tales.
3. Musical artist: The calypso genius Mighty Sparrow is usually thought of as coming from Trinidad, but in fact he was born in Grenada. Here is a YouTube clip.
4. 19th century Haitian revolutionary: Henri Christophe was born in Grenada.
5. Movie, set in: I can only think of one, namely the 1957 Island in the Sun, starring Harry Belafonte, which is well known for its early portrayal of an interracial embrace. I haven't seen it, but I guess I like it in principle. Much of it was filmed in Grenada as well.
The bottom line: For an island of about 100,000 people, that's not bad.