Yes, three times in fact.
No, Illinois has never won the NCAA Men's Basketball Tournament.
No they have not.
Twice. In 1980 and 1986.
No. The Drexel Dragons men's basketball team made it to the second round of the NCAA tournament in 1996 but were defeated by Syracuse.
yes in 1993 they lost horribly to Louisville
Georgia made it to the Final Four in 1983.