nothing is specified, we are left to wonder, tho maybe be related to she having affairs.
Yeah, the agency one is likely 99% certain it was a sexual scandal given the hints about MinJee's past.
Although given she's been dating Daeshim since high school that leaves her a small margin of time for having dated Liam unless she was fucking since like 13 (which is very possible in today's day and age) since that would mean she likely started dating Dae between 15-17 years of age most likely. IIRC she pretty much tries to evade the question of when did she date Liam/why Daeshim didn't know about him, so although its very vague there is the possibility she was two timing when she start dating Dae but then broke up with him and became exclusive to Dae (or at least tried to, would be more accurate).
NTRman really needs to clear up shit like this, I love "read between the lines" type of things, but I love them when they're things that are pretty much indirect/borderline confirmations for those who pay attention, not when they're just "could be this or could be 10 other different things, make of it what you will" which just leaves us with the doubt lol.