From the original book and game, there were 5 students who are friends, it includes: Hwan's father, Woo Hyensung (they changed it to Byeon Woonjong in the drama) + 3 other boys. They used to hangout at the detention classroom when it was a music classroom before. But a bad incident happened which involved the principal. 1 boy went missing while Byeon Woonjong got admitted in the hospital. Hwan's father tried looking for the missing boy and that's when his time loops began. But he failed which made him lost his memories. After it, he also lost his mind and got worsen as a person.
While in the drama, they changed it to only 4 students and added the plot about the scholarship program, it includes: Hwan's father, Jooan's father, Cein's mother and Byeon Wonjoong. It looks like Hwan's father and Cein's mother used to like each other. But a bad incident happened which involved the principal. I think he's the one who assaulted Cein's mother. It also looks like the principal manipulated Hwan's father. That's likely the reason why Hwan's father failed on his time loops. He sided with the principal, backstabbed his friends and also seems to have a part on their tragedies. In the end, Cein's mother is suffering from depression and constantly suicidal while Jooan's father was also suicidal who turned into alcoholic, he doesn't trust anyone and afraid of being alone to the point he gets violent. I think they were traumatized of their past incident. While Hwan's father forgot about them and grew into a corrupted politician who is still continuing his ties with the principal.
Byeon Wonjoong is the dead man on the beach. He talked to Jooan's father that he died several times which implies that he also went through time loops and he could possibly be the suspicious man trying to save Cein's mother from the fire incident. The clear part is, he has a big role for being the one who wrote "The Note" about the future events of the boys. My theory is, before he lost his ability and memories, there must've been a timeline where he followed the boys in the future and wrote about them. He acts as a guide for them.
The mistakes and tragedies of the adults are unfortunately being passed down to their children. And now, it's Hwan's turn to do the time loops in order to save his own friends and not make mistakes like what the adults did. The big difference for Hwan is, he has friends to support him unlike his father who was alone when he did his time loops.
Hopefully, Season 2 will come.