For the Army of Arm Chair Psychologists...

Stockholm Syndrome would only apply to people who didn't have feelings for someone beforehand, whereas Bum had feelings for Sangwoo from a distance for like 3 years. Bum was already an atrociously abused, self-harming and self-loathing loner, so he saw Sangwoo, one of the only people who saved him from abuse in the military, as his only option for happiness. Of course, Sangwoo also turned out to be abusive, but after already suffering so much abuse, he chose to look past it because Sangwoo was the last thing that kept him going anyways and they discovered that they shared similar abuses which they dealt with in different ways (Sangwoo by hurting others, Bum by hurting himself).

As for Sangwoo's oedipus complex, yes, that was clearly the initial reason for his feelings as Bum felt like a replacement for his mother (which was why he stopped having the waking nightmares about her). However, once Sangwoo and Bum began bonding over the understanding of their shared abuse (Sangwoo's dad and Bum's uncle), that is when I think they both began having genuine feelings for each other. Also, since Bum's uncle reminds Sangwoo of his dad (who was his first kill) I believe he thinks that killing the uncle with Bum would be like the ultimate bonding experience.

I don't think that Sangwoo was telling BUm not to trust him in the last chapter because he wants to betray him, but because he actually cares about him and knows that his violent tendencies and psychotic episodes may actually lead to him hurting Bum (which he genuinely doesn't want deep down). But that may be end up being the reason that Sangwoo wins his bet and doesn't grow old, because maybe after killing Bum's uncle, he'll start having delusions of Bum being like his mother after he killed his father, when she started to hate and abuse him as well.

While he and his mother once sought to comfort and shelter each other from his father's abuse, once he killed his father, the pent up anger and violence his mother received from him was transferred to Sangwoo. He might kill Bum (just like he likely did to his mother) in anticipation of a betrayal which he was taught would happen after an abuser has been dispatched (main theme of the story being the transfer and lasting effects of abuse and the way that the abused go on to use abuse as a learned defense mechanism from more abuse, even from those who wouldn't abuse them because they can't bring themselves to trust anyone) and after realizing what he'd done, kill himself. But that's just another theory.