Woojoon behaves quite credibly as an extraterrestrial would, in a sense. It (not gonna use "he" since it could just as easily have borrowed the body of a woman) has a completely different set of moral principles, so it doesn't even understand why it's "wrong" to take Hyunsoo's body without permission.
Or rather, it knows about asking for permission, but it only sees value in doing that when the body in question belongs to Hayeon, with whom it has established a relationship of mutual curiosity. Otherwise, it probably never considered asking Hyunsoo to use his body, since it's probably not even aware he belongs to the same species as Hayeon. (And so what if he does?) It probably only detected Hyunsoon as a life form of commensurate size (it didn't seem to know anything about the shape until Hayeon showed it the mirror), with a brain capable of articulating the same language, conveniently close to her.
Or it could be a clone. After all, Hyunsoo had left the classroom before Hayeon did, so why did he come back there? Did the possession take place right after he left and Woojoon come back to the classroom because it knew no better than retracing his steps to find her? Or did it make a double body and placed it in the classroom in the hope she would still be there or come back at any moment?
The reason I don't think it's a clone is that Woojoon doesn't seem to know much about it. How would it make a clone without knowing what it would look like, and even give it clothes if it doesn't understand what clothes are? I think possession is more likely.
My hunch is that Woojoon isn't a corporeal being, or if it is, the body isn't anywhere close. I don't think we'll see spaceships and some crazy-shaped entity. It must have contacted Hayeon telepathically and be able to lodge its consciousness in any creature whose brain can take it.
I'm probably overthinking this, and we'll only get the romantic part from now on, but it's fun nonetheless.