Anya meets Kirill in a bar, and the next day learns that he is her teacher. There can't be any relationship between students and teachers, which means she has to lie. Fedya jokes about Polina that she works all the time while he lives an active nightlife, and the girl decides to teach him a lesson.
A religion is a belief system with rituals. The missionary kopimistsamfundet is a religious group centered in Sweden who believe that copying and the sharing of information is the best and most beautiful that is. To have your information copied is a token of appreciation, that someone think you have done something good.