Points Scored, Season (14 games) 716 - Oklahoma 2008
The most points scored by one team was 222 by Georgia Tech
I believe it was Prairie View A&M in 1991, with 617 points scored against, or 56.09 points per game.
In Division 1-A, that was when Michigan State, losing 38-3 to Northwestern in the 3rd quarter, scored 38 unanswered points to win 41-38 on October 21, 2006.
Oklahoma holds the NCAA record for the most points scored in a single season with 702 points through 12 games in the 2008-2009 season, which is 58.5 points per game
Wyoming scored 103
Bevo Francis holds the record for most points scored in an NCAA basketball game with 113, set in 1954.
She scored 47 points
Jack Taylor of Grinell college scored 138 points.