1: Man, what an avant-garde US artist! (3)
2: Dozens of sprites seen on Tuesday and Wednesday initially (7)
3: A country, one said, in trouble (9)
4: Pitcher, lunatic, not married (5)
6: Odysseus' first requirement - to catch you like Polyphemus? (3-4)
7: Corpse apt to turn up in science fiction (5)