Yes, all are correct. We beat Rice in Omaha in 99, they beat us in 06.
Cal St Fullerton beat us in 04.
We dominated Stanford for the national title in 01 (hard to believe it's been 20 years). Stanford's last win in Omaha eliminated us in 2008.
South Carolina eliminated us in 04. We also blew a 9th inning lead against South Carolina in the deciding game of the 2002 Super Regional when we were an underdog 3 seed (not 3rd seed overall, 3rd in our regional) who upset Florida to win the Gainesville regional that year (anyone remember Jim Burt's heroics in those games?)
Anyhow, I hope you all enjoyed trying to guess these teams.