@LysandersTreason Its quite hard to understand without reading the novel. The manga skipped past this part really quickly and basically left out a whole day of events.
The basic outline is: MC coincidentally meets Rose, they go get lunch, meet Ikeman's group and disband. No karaoke.
Next day, at the rooftop, Ikeman asks MC if MC has a relationship with Rose and MC denies it, but just like in this chapter he uses the words 'that woman' when referring to Rose. Ikeman gets mad, shouts at MC and leaves. Nothing new.
But the next day, after school, Rose waits for MC and decides to walk home with him. Ikeman sees this, gets jealous and only now does he invite her to karaoke.
Next day, MC is working on the 10 signs he has to write, Ikeman pulls him to the rooftop again and tells MC that he 'did' Rose after the karaoke. Nothing really happens and MC returns to class. He starts thinking about his future and how bleak it will be with nobody beside his bed at his death and he decides to become more proactive by trying to help his classmates. He gets rejected and realizes that his appearance is at fault, but the class prez does not confront him, he just goes to the bar and gets work from Marquis. Also, there is no rock band guy yet, and I don't think there will be since the novel already moved onto the events of the day after where this chapter left of.