So sorry it took so long!
-First off, I think your cover needs a bit of work. Until I clicked on it, I couldn't even tell what it said, which defeats the purpose of having an eye catching cover which draws people in. Even now, I can hardly read it.
-I'd suggest you not putting the description of Christine's face in quotations; it blends in too much with the dialogue. I'd put it as an I-cannot-believe-you-just-did-that face or put it in italics. In addition, you need a comma after "say" in that line.
-You need a comma after "people" in the first line of the next paragraph.
-Semi colons are only used to join two closely related sentences which could stand alone if they had to. Therefore, it'd be better if you had, "The people I hit - they don't..." or "The people I hit, they don't..."
-There should be either a semicolon or a period after "personalities" in the last full paragraph or else it's a run-on.
-The first line is very choppy. You make the reader pause a lot with all the commas, and they're not all needed. You could easily take out at least the one after "happened."
-"Reverberate" isn't the word you want when you're talking about her head on the pavement. To reverberate is usually associated with a loud sound, but in such a way that the sound is what's causing the vibration. It doesn't exactly fit the image that you're going for.
-The line, "All my hopes, that maybe I was kind..." if you're going to have a dash before "well," you should have a dash to start the phrase after "hopes."
-"...boyfriends after me - they'd also called the police..." I would take out the dash and make it, "...me, but that they'd..."
-Also, if they just saw her kill somebody with little remorse, would they really chase after her? Unless they're oddly brave, it seems like a stretch.
-You repeat "ran" in the same line twice; you might want to come up with another word.
-You don't need a comma between "lift" and "so."
-You do need a comma after "Fuck off."
-The police probably wouldn't volunteer all that information. I don't know how it is where you are, but typically, they'd just read them their rights and wouldn't say anything more than what they're being arrested for.
-It should be "my mother and I" when talking about the flat.
-You don't need commas around, "as Mum hurried down the stairs," but you can't have both that clause and "while I..." without some kind of conjunction, probably "and."
-When the police realized that they couldn't get her out of the elevator, they would have undoubtably started up the stairs, meaning that if they hadn't reached the flat by the time she and her mom were leaving, they definitely would have met them on the stairs. They wouldn't just give up.
-You repeat "her eyes" in the beginning of three consecutive sentences towards the end of the chapter. You might want to rephrase some of those.
-The line which says, "If I had a personality disorder, people would probably understand me more." sounds wrong to me. Wouldn't having such a disorder make her harder to understand to a normal person? I think what you mean to say is, "If I could define/describe my personality disorder, people would probably understand me more."
In conclusion, you have a pretty interesting start, just remember to keep it realistic and not to rush things. Your main character is certainly intriguing, just be sure to decide on either the ruthless killer personality or the slightly insane personality, or whatever you choose, and stick with it. I feel like it would be easy to slip out of character with her, and you want to be consistent more than anything. Keep going, though!