No, Mikan played with Slater Martin, a Texan and Hall of Famer, and I believe atleast one other, but I'm not sure.
No, Hakeem Olajuwon's first title in '94.
"Hakeem was at the pinnacle of his career. In that year, he became the only player in NBA history to win MVP, Finals MVP and Defensive Player of the Year in the same season. Olajuwon's fame was well-deserved, as the Rockets team was probably one of the most lightly-loaded championship teams of all time. Neither the other starters (Robert Horry, Otis Thorpe, Vernon Maxwell and Kenny Smith) nor sixth man Sam Cassell were considered stars at the time, documented by the fact that Hakeem was the only Rockets All-Star player that year [3]."
Now you can almost argue that Horry will be in the Hall of Fame, but not for the conventional reasons, he's just hit big shots at big moments, and in no way lead any team to a championship.
You might be able to argue that the Pistons team that won it a couple of years ago won't have anymore then one Hall of Famer on it, but I guess we'll have to see how that plays out.