Very interesting interpretation and I think you more or less got the story, but I think you're incorrect on a couple of points. I watched the movie and was completely confused, so I went to this forum and read some clues, then I re-watched the movie paying closer attention to the certain scenes and watched the cast interviews and the deleted scenes. There are some clues in there that helped me a lot as well. So I finally think I have the (more or less) cohesive story.
- Kang, as a young boy moves to a new school, with his father who teaches there. They live in the forest. His mother left them earlier.
- Kang befriends Min, who also live in the forest. She lives with her mother, her father rarely visits them. Her mother is rumored to be a whore who sleeps with the local men.
- One day she takes him to her house (I double-checked on the second viewing, its definitely her house not his). They hide in this little room above the living room. They witness her mother having sex with another man. Then all of a sudden her husband returns and kills both her mother and her lover with a sickle (important clue right there). Kang makes a noise and the children flee, chased by her husband. Kang falls and hits his head which knocks him unconscious for hours, if not days (note how he wakes up in the dark.) Because of either the shock of what he's witnessed or the head injury, "he was sick for a long time" and loses his memory. It's not clear what happened to Min, but let's assume she was killed by the husband and he got rid of her body along with her mother's.
- Kang and his father move shortly after, eventually his father opens a photo shop and Kang grows up and moves to Seoul.
- He meets his wife and gets married (played by the same actress as adult Min - something I totally missed on first viewing, it's not credited but watch cast interviews on the DVD). I think her being played by the same actress as Min is a very important part of the story and is a major clue in itself.
- As an adult, Kang still suffers from the childhood trauma, he has frequent migraines and memory loss, sometimes he loses track of time and can't remember yesterday (watch the deleted scenes for an important clue). He has vague memories of his childhood and of what happened in the forest but can't remember any specifics.
- His wife dies in a plane crash
- In a vigil for the crash victims, he meets a woman whose father also died on that plane - later they meet again and she (possibly) becomes his girlfriend.
- After his wife's death, he becomes emotionally distraught and drinks heavily. He tries to forget her and move on with his life, and finds a new girlfriend (I'm actually not 100% sure if the girlfriend was real or was only in his head).
He proposes to her in yet another attempt to start a new life (watch a deleted scene).
- His condition gets worse (frequent migraines and amnesia), exuberated by the heavy drinking. He makes a major mistake at work and is asked to take a leave of absence. He's haunted by the childhood memories so one day he drives to the forest to re-visit the place where he once lived. He's either drunk at the time, or is having one of his migraines so he's not thinking clearly. He wonders around the forest, eventually stumbles into the tunnel and is hit by a car and that's where the movie begins.
- In the hospital, he's having a near-death experience. It's pretty clear, especially on the second viewing, that everything we see after doctors start resuscitating him is a dream - until he's back on the same table at the end of the movie with doctors still trying to revive him.
- In his dream, he remembers Min, who comes back as an adult to tell him a story of what happened when he was a child and why his memory is such a mess. He also imagines a lot of events that never happened (such as him killing his girlfriend and the TV exec).
- As he finally remembers Min, she is no longer a "lost soul" and according to the legend is now free. He is also free now as his memory is back.
- As the doctors finally give up on him, he's at the end of his dream, and as he imagines Min taking his hand, he returns to life (she leads him back to reality). He suddenly regains his pulse and is back from the dead. He wakes up after the surgery and sees a child in the same hospital room (possibly himself as a child?). The end.
Just a few more closing thoughts, to clarify a few points...
- Kang didn't kill anyone, it was all his imagination inspired by what he'd witnessed as a child
- The phone calls were a fantasy along with the letter
- His wife really did die in that plane crash
- I'm not sure if "the girlfriend" was real. Watch closely the scene near the end where Min turns into her for a brief second as she takes a bandage off his head. This is right before he goes through the cave to open the door into the tunnel. So she might as well be part of the fantasy. He met her for real after the plain crash and imagined the rest.
- The cop (his friend supposedly) was probably not real either.
- Obviously Min never grew up, so the adult Min he imagined in his dream is actually his wife - she is played by the same actress!
I agree that this movie is a real exercise for your brain. We were given a confusing story with a bunch of clues carefully concealed, how to put them together, is up to a viewer. I feel like I just solved a puzzle! :)