I assume, going by the logic of this manga so far that somehow she saved the girls life with that box cutter while also resolving some personal issues in the process.
The blood on her hands is almost definitely her own. It's a universal constant that you will cut yourself when you use a blade if you haven't been trained in bladed combat.
Money's on Satsuki covered her in her own blood to make it look like she has a head injury to keep her indisposed. Can't die on the roof if you're passed out at a hospital.
It doesn't make sense for her to kill her as she would have died anyway (if Satsuki's premonitions are correct) and by killing her herself instead she's risking jail time. Wonder what the heck happened there. I guess she made her pass out so she survives the death from premonition while at the same time making her too scared to bully Komachi again.
Yeah, looking through the pages again, I think what happened is that Satsuki just knocked her out, then cut herself and spread the blood around to make it look worse. The bloodstains on her hand look like they would come from a cut on the hand itself rather than a Extertal source too.
That way she would both prevent her from actually dying (due to not being were the premonition said she would die at the right time), and possibly scaring her enough to stop the bullying.
Her just suddenly turning into a murderer doesn't really make sense, and we already know she stopped caring about her own reputation anyway.
@GoldenGummy
She's called "liar satsuki" because her premonitions never come true ('cus she stops them). Komachi being alive is a big deal to satsuki because Komachi is surprisingly nice to her. The girl is too nice though, so equal possibilities that she will personally mess up satsuki's life or that she's something unholy enough to disturb fate.