The doctor, Yo Han, can't be Jae Hoon. I mean, his mother seems alive (she was alive when he was a teenager), and Jae Hoon killed his mother. So, Yo Han is not Jae Hoon. But Jae Hoon is the current serial killer (the religion, revenge and so on). So, we have to find who is "Jae Hoon" right now... I think I already guessed it, but since I want to be wrong, I'll not say it, hoping for me to be wrong actually...
Here some hinds : there were two mothers at the hospital. They both kept their baby. One of her remarried and had younger kids. They only showed us three corpses after Jae Hoon killed his family (it's important). The watch is an important element too.
There are more elements (I made some notes when I was watching the episodes, I have too much of them after only two episodes, damn...). But I don't want to spoil too much/point too many elements people didn't pay attention at and that will be used later.
I'm craving for the 18 others episodes.