Classroom rules probably translates to either правила класса or Правила в классе, right?
Правила класса is better.

"The office" is the office for the school (elementary, middle school, or high school). There at a minimum will be found the secretary and principal, plus sometimes a counselor and possibly vice principals. Large schools in the USA may have several secretaries and a number of counselors.
I think, analog in Russia is учительская. Yes, a teacher can bring there a pupils who have bad behavior. In учительская you can find teachers (учителя), head teachers (заучи - usually, pupils are most afraid of they) and sometimes secretaries and директор (principal).

If it is a university, it will be named кафедра of institute. Rector is in ректорат. For example, our university has more than 5 institutes and each has it own кафедра - кафедра психологии, кафедра физмата (физико-математический институт) etc.