I'm sorry you're going through all this. I recognize some of those characteristics in myself. The impulsivity, difficulty paying attention, getting tasks completed, sitting still etc.
However, like a previous poster said, it sounds like there's a lot more going on. A lot more. Just an opinion, but it does sounds like maybe oppositional defiant disorder or borderline personality disorder. Most people who self harm end up eventually being diagnosed with a personality disorder, most commonly borderline personality. Maybe something to look into. Is she in therapy? On meds at all? Does she see a psychiatrist? It sounds like you're in the UK? I know things work a little bit differently there (I'm in the US).
Again, this is just an opinion, but if my child was going through all that, I'd have her in therapy ASAP.