I’m not saying you don’t have some important points but re your first daughter: some months have more than 4 weeks, but with yom tov and vacations, some have less and it may actually work out to your daughter’s benefit. Am I missing something?
About the second, and utilities for the lights: that’s absurd. I would think that if the school had such a policy they were obligated to make sure your daughter knew when she asked permission to tutor.
I hope everything works out well, and thanks for sharing. We have learned from their experiences.