I reckon the project is perfectly do-able, but would take a lot of effort, and if you are not familiar with PICs, domestic IR remotes and RTC already, then you have a lot of learning to do.
What make of TV is it? If it is a Sony, then the IR protocol is simple, and the protocol is well documented and understood.
What view do the governors have on you taking the new TV apart? I would worry about breaking the TV with all of that messing about.
Hope you have plenty of spare time.
What languages, PIC compilers PIC chips and programming hardware do you have available. I have MikroC code for PIC18f45k22 that does a lot of what you want, but it is of no use if you do not have MikroC Compiler.
EDIT: Why not just run a CCTV feed through to the principal's office, so he/she can monitor all forms of misbehaviour?