are teachers allowed to make fake profiles on facebook?

[FriendlyConqueror468]

in our school's and surrounding school's network of Facebook, there has been a lot of fake profiles adding people at these schools, and me, Facebook friend requests. the profiles say they attend out school, but the pictures are always of girls we don't know. so we conclude that they dont go to our schools. so some girls mom is the principle and she said her mom was doing it (well THE GIRL did not say her mom was, its just a rumor). in the last 6 months there have been about 20 of these "fake" profiles we think are teachers disquised so they can look what we post, the pictures we are in(if we are drinking/smoking weed. etc...) so is this legal for teachers to do this? because firsthand I have known teachers that i wanted to add but they said it is illegal to add us until we graduate....so can someone clarify?

thanks for answering! feedback is greatly appreciated!!