RE: Scrutiny of Individual Schools
Back in the day the Schools Organisation Committee (or equivalent) could do this but now you're on shaky legal ground even for a maintained school. Post-2005, even maintained schools are broadly "independent" of direct council control and it is difficult even for the director of education to "haul in" a head or chair of governors of a school that's behaving poorly.
If you were going to do this I would suggest delicate handling - starting with an informal discussion with the chair of governors. It might be better to do any work jointly with them.
Of course, if problems in performance relate to the governing body...
Consult the monitoring officer and the director of children's services - they should be able to give you a steer as to whether this is appropriate.
As usual, what will happen now is that someone will come along saying that they did something like this only last week and it was a fantastic success. Damn my imperfect knowledge of scrutiny.