I actually really like this manwha specifically becuz most average drama webtoons would make onyu and cheri fight and have friendship rifts constantly but they truly care about each other and their bond transcends any messiness from ilmi and her pussy parade because of the implicit trust they have in each other. Maybe they will have a big fight in the future but I'm glad it hasn't happened cheaply in the story yet.
Most webtoons would also have Cheri just be an evil shallow popular girl trying to make herself look good by sticking to Onyu but her character is much more layered and complex than that and their friendship is genuine.
My guess for Cheri's past is that she either got bullied or was a bully at her old school (based on the way she reacted to bob girl telling them she got bullied for her weight before) and that she got plastic surgery to escape from it and obsessed with the way she looks (which would explain her ed). Or it has something to do with her mysterious family. Or both.