
True, it does sound out oh character (unless it's a mistake of Google.translate).

The thing is, Dohyun has lost all hope. From the beginning, he's been going day to day with the assumption that once Sungho completed his revenge, he would let him go. That's why he gave in and became compliant after finding the notebook, because he had a set goal to work towards, and he knew that the suffering would eventually be over.
But things have changed now. It isn't just about revenge anymore, because Sungho /likes/ him. When it seemed like he hated hated him, Dohyun had no reason to think Sungho would keep him around once he was done with him. But, if Sungho likes him, there's no promise that he'll ever be set free. :(

I don't understand what Dohyun being selfish and not caring about others has to do with it. He's tired and there's nothing but more suffering in his future. In his situation, suicide is one rational choice.

Dohyun's attitude changed after Sungho said, "I like you." He always believed that Sungho hated him and did this out of revenge, which meant once the revenge was done, Sungho probably would let him go. Since Sungho was not motivated by revenge, Sungho would keep him around. You can notice that only after Dohyun looked around the warehouse that his eyes became very dead. He did not want to spend the rest of his life there and death would be preferable.
It was a momentary lapse in his mental state after getting strangled. He probably thought that he wished he didn't wake up from it. I don't find it out of character at all.

Well i think it's just an act. First of all dohyun asked sungho to kill him after he sees the cake, like he just realized something. So i think he has some kind of plan. That's why he asked sungho to kill him to confuse sungho. But why would he take the risk to say that? Because maybe dohyun realized that sungho actually doesn't want to kill him. As you can see after thinking he killed dohyun, sungho Immediately became shocked and regretted what he did. So maybe dohyun realized that and tried to take advantage of the situation. well yeah that's what I think :v (sorry for bad English btw)

In chapter 32, Sungho smashed the cake and said that's what was going to happen to Dohyun after the revenge was complete. Implying that he has intended to kill him after. So Sungho isn't going to let him go after all, maybe Dohyun's just given up and wants to die sooner rather than later.
Isn't it out of character that Dohyun wants Sungho to kill him? He was a badass until the last minute. He is the kind of person who doesn't care about others. Such people don't want to die. People with self destructive behavior want to die. Sungho would be the candidate for saying "Kill me". The past hurts him the most. Dohyuo didn't remember until some days ago. Getting strangeled isn't really an excuse for it.