This movie is more into psychological horror, it has interesting story but poor telling. And since i can't find any satisfying explanation i want to try explain some point. Excuse my raw explanation and untidy English.

So there are two main characters here, student Ha Young and vice principal Eun Hee.
As for Ha Young's story, her best friend Su Kyung was dead suicide (the very first scene) after being sexually harrassed by teacher Park and is ashamed of herself. She'd rather die than being insulted her for what happened. Ha Young can't take it and seek revenge trying to kill teacher Park but ended up being helped by Eun Hee.

Eun Hee's story is a bit confusing. Her trauma started in 1980, when she was a student at that exact same school. The soldier's appearance was related to Gwangju Uprising incident in 1980 (Try search it). The students all supposed to be at home, but at school there were still the security guard, Eun Hee, and Jae Yeon. The securiy guard is dead shotted by the soldier and then several incidents happened. Because of these incidents Eun Hee developed trauma that make her forget what happened and mixed her memory.
In throwback scene, it was seen Eun Hee was the one hiding inside the classroom while Jae Yeon was the one attacked by the soldier in the toilet. But it's actually the opposite (as stated by Eun Hee's psychiatrict 'It was you'). Hence, the one who was hiding in classroom and taken by the soldier's vehicle is Jae Yeon (because there is also a scene where Eun Hee visited unnamed grave, thats the missing Jae Yeon), and the one hiding on toilet, sexually harrassed, and stabbed on the hand is Eun Hee.

The murders was all done by Eun Hee. But the only murder she 'conciously' done is teacher Park, while the others was done by her unconcious self, as it was seen on the last part, they were killed by Eun Hee while wearing school uniform (indicating her old self seeking for revenge).
Principal was killed because she kept threatening others to keep silence about school's incidents (First incident in 1980 as Eun Hee's ex homeroom teacher and the second incident that i believe trigger Eun Hee to kill her is after her encounter with teacher Park's in his home).
Meanwhile, the headless uniformed person i think is the same person in the very first scene with the window incident (not the old security guard in throwback scene). I still dont really understand what happened to him, it could be accident but the last scene somehow indicates Eun Hee is the one killed him (but for what reason?). His head is inside the bucket full of disgusting creeping animals, while the body is hid on the roof with the soldier's nametag on his wrist. Maybe his dead is Eun Hee's way of revenge toward the soldier? because they are wearing 'uniform' (remember the scene when the soldier's uniform is blurred by black thing in late scene)

And the ghost that keep haunting Eun Hee, i think she's Eun Hee's portrayal of deep regret and guilt toward what happen to Jae Yeon, whos body never found, but in herself form. The ghost has half shoes (Eun Hee running away to toilet from soldier is in one shoes too). But why one eye stabbed? I dont really understand too.