#1 is interesting. Here is a map showing which schools were selected as peers on a Chronicle of Higher Education Survey.
Who Does Your College Think Its Peers Are?
Observations:
1) UConn only selected one Big 12 school - Texas. 3 Big 12 schools listed UConn - Iowa State, Texas Tech and WVU.
2) Iowa State listed everyone in sight, including Cincinnati, South Florida and Houston.
3) Houston didn't list any Big 12 schools but did list Memphis and Louisville.
4) Brigham Young was only listed by 5 schools - its own satellite campus in Utah, Pepperdine and 3 branches of the University of Phoenix. If they aren't selected by the Big 12 it's going to be due to the feeling that BYU is not a compatible institution.