Is it permissible for me to photocopy students' exam papers in my library? And is fatlah (facial threading/hair removal) forbidden for women, even if she has a mustache?

If you photograph small papers for students with the intention of cheating in exams, then this is forbidden (haram), because it is considered aiding in sin and transgression. You should advise and warn them against cheating. However, if they photograph them for a permissible purpose, there is no harm in that. There is no harm in a woman plucking hair that is permissible to remove, such as beard hair or mustache hair.