As thanks for all the support on my theory, here's a little more of my thoughts, and an extra point I figured out just now.
I actually think that Guwon could have put down Heos father, after he turned into a zombie. Which would explain the split head. So, Heos father's cause of death, strangulation by Heo, cause of second death, blunt force truma by Guwon.
Honestly, I have suspected Heo of doing something or going through something since his first flashback, during Guwons zombie beatdown. He immediately identified the person in the memory as Guwon by eluding to the fact that he had seen the same scene before. I did a double take and was like, wait, those aren't Guwons arms though? Since then, I have given amnesia baby a sideways stare, wondering what he actually did, and why he unsettled me more than Guwon at times.

This is my theory. I think Heo killed his father. In one of the previous chapters, Heo has head pains and a flashback when Guwon beats a zombie to death. In the flashback, we see arms beating either another person or a zombie. Importantly, the arms we see, are not Guwons arms, they are white.
I think Heo killed his father, and I suspect that the person hitting someone in his flashback was his father, and that his father could have been beating Heo, possibly over food or lack of resources. I think his father may have tried to kill him, and Heo killed him is self defense. Due to the traumatic nature of this event and the injury he sustained, his brain got rid of it. The memories being triggered by similar actions carried out by Guwon, is due to Heos guilty subconscious possibly linking him and Guwon as the same, even if the instances weren't.
This is further supported by the flashback from the last chapters showing Heos shillouet possibly strangling something.
I believe think it is feasible that Guwon didn't kill Heos father, and that it is possible that Guwon may have seen Heo kill his father. It would also explain some of Guwons favoritism to Heo as well, especially when we have the context of him treating the hounds well, due to their fighting prowess.
I do also think the reason Heo may have killed his father could be more fucked up than self defense, I'm actually certain it is, but the above theory is me giving Heo the benefit of the doubt.