Fridge Brilliance: There's actually a good explanation for the school's uncanny ability to turn good girls who should know better into proper St' Trinian's girls: all of them came from restrictive or outright abusive environments, and at St. Trinian's they invariably find people who let them be themselves (Annabel Fritton, in particular, had been bullied at her past school and saw St. Trinian's headgirl knocking out her bully).
Just what is going on between Matron and Camilla Fritton? They do seem to be very close. It's Matron's hand that Camilla clings to when she's upset at Mr. Darcy's funeral. Matron is also seen walking along arm-in-arm with Miss Cleaver, the sports teacher.
There seems to be some of this between Miss Dickinson and Chelsea Harper during the scene where Miss Dickinson discovers the girls have been cheating at School Challenge. She tells Chelsea that she's been watching her with her feminine wiles and her "saucy ways", and reassures her that being smart is "very, very sexy". It does seem a little like she's attracted to Chelsea.
In one of the deleted scenes, Chelsea offers to try seducing the Cheltenham Ladies' College team in the School Challenge final; and when one of the other Posh Totties points out that "Cheltenham is a ladies' college, Chelsea!", her response is a shrug and declaring, "I don't mind giving it a try".
Unintentionally Unsympathetic: The girls forcing Annabella to run naked and livestreaming it is a lot less of a cute harmless prank and more like a cruel and horrible case of bullying today, especially since they receive no comeuppance for it and she later befriends them with no hard feelings.
What an ear worm.