Honestly I'm sticking to my position that she'll find out he's not a student in episode 6 or maybe at the end of 5.
Then I don't know how they're going to tell her he's an NIS agent and that he's there on a mission, all I know honestly is that I'm sure she's going to help him with his mission, which is why I think the high school will find out by episode 7-8 that he's not a student.

She is def an agent, too. 

#1. She suddenly flipped a guy 

#2. Her name is Bong Ja in the flashbacks, not Su A. 

 CherryBunny:

She is def an agent, too. 

#1. She suddenly flipped a guy 

#2. Her name is Bong Ja in the flashbacks, not Su A. 

Her being agent doesn't make sense.

Let me give you explanation for your reason to think:

#1. It is the common self defence from what I know so flipping guy is not a big deal.

#2. People can change name, I mean criminals can so why can she not  💁 if she want to. Most of the people around her know her previous name and she mentioned many times to not call her that name which directs it to the fact she doesn't like that name so that could be the reason she changed it.