I have to be honest, I don't think you should be analysing her past and her current behaviours to the nth degree like this. It really doesn't serve any real purpose. It's a very cold and clinical approach which gives no real insight into her personality.
Thing is, most of us would look a bit odd of our pasts were analysed like you've done. We've all had ups and downs and we've all had learning experiences. But it's who we are NOW which really counts.
Also, in the last paragraph, your description of yourself gives us no real clue as to whether or not you're a good catch. Again, it's very clinical and gives no real insight into why a girl would want to be with you. For all we know, you could also be a workaholic with no friends (not suggesting you are!)
And just for the record, the reason I've started my post with these points are to get you to re-examine how you look at both yourself and a potential girlfriend.
Anyway, whether to stay or go isn't about who your girlfriend is....instead, it's about who you are and what you want from a relationship. It's as simple as deciding whether or not your needs are getting met.
Does she make you happy? Do you feel good about yourself when you are with her? Can you imagine yourself growing old with her? Do you love her? Do you trust her? If you've answered "yes" to all these questions, then I say you should continue with the relationship.
When you're only been dating a few months, it's hard to really be objective about a person. You're both acting on your best behavior and you're probably at this point only just beginning to figure out who she really is. It's not good to be feeling very serious in that short a time.
Her past sounds like there's been tons of drama. A suicide attempt, lots of drinking, she's been violent before, lots of one night stands with guys she's still in contact with, secret meetings that you're specifically not invited to. It's not normal to claim a guy is "like a brother" and then carry on with getting all touchy-feely with each other. I seriously doubt she would actually do that with a real brother.
I see tons of red flags here. I've seen this exact sort of behavior before and it didn't end well. It doesn't sound like she's out of the "bad girl phase" at all. and if this is how she's acting in the early honeymoon phase of your relationship, then I'd hate to see how she acts later. If you are going to continue seeing her, at least try to not feel too attached as there's a good likelihood that she'll end up cheating while she's away living with the guy who has a crush on her. Also if she suddenly turns up pregnant, make sure you insist on a paternity test.
To be quite blunt, if this is your dreamgirl, then you have very low standards. I myself like someone who is financially responsible and has a job--someone who will contribute to a relationship. I chose a man who has left his past in the past. He does not remain friends with exes. He wouldn't be my boyfriend if he did that. If he was touchy, feely with anyone other than me, I would drop him like a hot potato. I rarely drink, and have chosen a man who doesn't drink much either. Having my man get drunk and violent is something I would never tolerate. If a man said to me he was leaving for six months to live with someone who has a crush on him I would say, "Have a good life. Don't stay in touch!"
I realize that everyone is not like me, but if you think you are worthy of a woman who will only flirt with you--someone who you can trust 100% and contributes financially to the relationship--a lifelong relationship where she will contribute to household finances and save for retirement, someone who will not take off for 6 months, when most likely it's not for a job (you didn't mention if it was), someone who doesn't have a drinking problem--then it's time to start looking for that person!
I don't know how you know so much about each of her previous relationships, but I don't think that either party needs to divulge each and every detail of a previous relationship. I only divulge, in general, a few of the main reasons why my marriage didn't work, and only ask one time a few things about my man's past, but not in such detail. After I know in general how they operated in the past, I don't want to hear about it anymore. Anyway, I hope you find happiness in whatever choices you make. Take care.