The first national basketball tournament was the National Invitational Tournament, the NIT. It preceded the start of the NCAA tourney. The first year of the NCAA Basketball Tournament was 1939.
No, Kentucky did not play in the NCAA tournament last year. They played in the NIT.
The Wisonsin Badgers played in the 2010 NCAA Men's Basketball Tournament.
Yes. The first time it happened was in 1980.
Michigan State has had 22 NCAA Tourney appearances. They curently sit 28th on the the all-time list.