Raskolnikov is strange, really strange

I honestly think the next person Raskolnikov is going to kill, if his sister does not let him go, is Luzhin. I am almost positive that if his sister does not follow his advice, he will kill Luzhin so he does not have to deal with him no matter what his sister's decision was. I was shocked that Pulcheria, Raskolnikov's mom, said Raskolnikov used to be engaged. Of course, she describes the girl as very ugly and useless, but the main point is that Raskolnikov used to be engaged. I found that kind of a shocker because since he is so socially weird, I would not think he would be capable of having a girlfriend let alone be engaged to her. His mom and the landlady did not want the marriage to happen, though. I found it peculiar that the mom said that Raskolnikov is like two different people and that he has always been like that. She says that sometimes he is goodhearted and intelligent and others he is cold and lives in his own world. I think Raskolnikov is so socially awkward precisely because he lives in his own world and almost never makes any connections with the people around him. I agree with her statement that he lives in his own world, in which he plans all his deadly actions. Razumihin, trying to be a good friend, decides that bringing women around Raskolnikov will help him out in a way.
Luzhin sends a letter and he says he wants to meet with them the day after but he does not want Raskolnikov to be present. I understand Luzhin on that part because Raskolnikov did insult him. The decision was left up to Dunya for Raskolnikov to be there or not, and she does want him there. I wonder why.
What I found sad at one point was that Pulcheria was afraid of Raskolnikov, her own son. I think she too believes her son has gone mad and she does not know what his next reaction will be since he has been so impulsive. Zossimov too thinks Raskolnikov is insane. Surprisingly, Raskolnikov is very kind to everybody this time and says he will go back to college soon (how old is he again? Did they ever tell us?).
His mom tells Raskolnikov that Marfa has died and Raskolnikov gets frustrated because he notices that everybody is afraid of him, and Dunya confirms this observation. Quickly, though, he regains his composure and actually apologizes for acting rudely recently but states that he is still adamant in not liking Luzhin. His behavior is so bipolar and weird!!