Also, you must consider, that our protagonist, obeys OUR RULES, but not those of THAT WORLD, a way of thinking something strange, but maybe due to the Korean discipline system... That explains why he killed without blinking in that world, and in ours world he lets himself be arrested by the police. You have to be stupid to not be able to analyze and reason this.
2.- About romance... Well, the protagonist is not dense, and I say this because he is not the typical Japanese protagonist, but wait, you will think at this moment: What the hell is this imbecile saying? I DONT see a romance tag!!! There is not tag because the protagonist is... ******
Well, as a small spoiler, our protagonist is not stupid in that aspect, that he avoids romance is for "something"... You will have to read it to know what I mean.