Sangwoo may have come to feel that Yoonbum is the only person he can honestly open up to & communicate with, so even on a selfish level he may have chose to keep him alive just to have someone to talk to....& he's probably become accustomed to his cooking by this point.
I don't think Sangwoo has even gotten the chance to consider what he'll do with Bum. He's been fighting the officer and then was dragged to the police station. So he really hasn't gotten the chance to think about anything else except how to survive. Although, I don't think Sangwoo will kill Bum, because I also believe that he likes Bum enough to keep him alive, but I doubt Sangwoo is going to let Bum go unpunished for not telling him about officer Handsome being in his house.
Officer Handsome.
I do think Sangwoo cares for Bum to some degree, but I don't think the reason he freaked out was because he was concerned about Bum's health. Don't forget that Sangwoo is a psychopath. There're two ways this guy reacts. Either he's irrational or he has a plan. In this case, Sangwoo probably realized right of the bat that he could garner the sympathy and empathy of the officers by making it seem like he's concerned about Bum's health. After all, what kind of kidnapper and murderer would worry about his victim's health?
By doing this, Sangwoo has laid out the trap to make it seem like officer Handsome was the one who hurt Bum and that Bum and Sangwoo are simply the victims of the deranged officer that broke into his house. He laid it on even thicker by making it sound like officer Handsome is Bum's ex-boyfriend and that he came after Sangwoo because he was jealous.