No that doesn't mean your school is watching you until they have security camera in your lab or they have complete log of your activities on computer(which if they have it will be of each and every user like you) .
if there is TV out on your ati card that means you can use your digital TV(or whatever ) in lieu of monitor as display unit and for TV in socket means you can watch cable TV (that coaxial cable going to your TV) on your PC by using that cable as input . OK