I can answer some of these questions with what I deduced based on implications in the story if you would like?
It was strongly implied that Joon was probably the murderer.
Duk-gwang was innocent of the murder (although he did beat the guy up beforehand).
That whole murder suspect fiasco/life story was what he was telling Sungho about in the cave.
Your first question takes a lot more explanation, but I'll try to sum it up as well as I can...
So... Joon was "forgiven" because Sungho basically bartered his life away to his father in order to get his father to stop going after Joon. Doesn't make sense at first, right? UNTIL you realize that Sungho did THAT because he was also bartering with Joon, getting his father to stop persecuting him in exchange for the knife that Joon had been planning on giving to the cops that had DG's finger prints on it from when he found and was trying to help the murdered guy. Joon was trying to frame DG, but stopped and traded the knife. So Joon never faced any consequences for his actions, but DG didn't get tried for murder. Sungho left DG on the island in order to save him from that.
i'm actually not content with how they glossed over the 8 year time-skip without filling us in about the murder case since it was a key part in the story. (why was joon forgiven? who was the actual murderer? what did dukgwang tell sungho in the cave? is dukgang innocent?) i have these fucking questions that the sex scenes didn't answer. is there a novel? can anyone please enlighten me(╯°Д °)╯╧╧