Yes the 1998-1999 Chicago Bulls. They are the only team in NBA history that won the championship and didn't make the playoffs next year.
No. The Rens played two years in Pittsburgh in the American Basketball League, losing in the preliminary round of the playoffs in 1962 and not making the playoffs in 1963. However, the Pittsburgh Pipers won the ABA championship in 1968 led by Connie Hawkins (who was also a member of the 62 Rens team before they folded).
Dallas 2011. Every Player won his first ring.
Vezina Trophy
The Oklahoma Thunder have not been in the NBA playoffs yet.
No 30 out of 30 teams that had a 3-1 lead in the finals won the championship.
This was the first unranked team to win the championship
The Stanley Cup.
A team gets the first round bye in the playoffs if it has one of the top two records in its conference.
Ben Roethlisberger
No
Bears 73, Redskins 0 (1940 championship game)