What should I do, and what is wrong with her?

This is kind of a long story but it will make more sense if I put in a lot of the details like these, I hope that someone can help me with this but anyway this is my story...I met this girl in late December on Facebook. I started messaging her on Facebook and I learned that she was a really cool person and we both had really interesting conversations and made each other laugh. We started to get deeper and deeper and she told me some of her personal problems with her life and such. I learned she had really low self esteem and self worth and she had some deep set emotional scars.
We would talk more and more and eventually on New Years eve I went to her house. I myself am a really shy quiet person so it and she had a group of people over, so I was friendly but quiet. She was really really sweet and gorgeous and she tried really hard to make me feel comfortable. At the time I was nervous but in retrospect it was really sweet. She was friendly the whole time, and when I had to leave she walked me outside and gave me a hug and I was going to visit later that day (had to work so I couldn't stay) and I left. When I came back later that day, I had a few more times alone with her and we talked and connected. I was still pretty quiet but I was getting better. She is kind of a goofy/funny girl so she made jokes and she'd wear my shoes and joke around with me, it was cute. At one point, she actually invited me to move in with her and two of her others friends that I knew pretty well (we had a lot of mutual friends). It was surprising but she was serious and I felt good she offered. I left that day and we still talked a lot on Facebook but there was an incident where she was trying to cut me off because she felt like I didn't like her because I didn't talk much so she was short/dry talking to me and she made a status saying "That moment, when you slowly end the conversation and never talk to that person again" and then later posted a status saying "I feel depressed and sick " Then I sent her a really long message describing my feelings and how I really liked being around her and she understood and started talking to me again. It was a close call but I heard from a friend that knew her that she just really felt like I didn't like her and due to past relationships, she has paranoia about that. Anyways, we decided to hang out again soon and I was still a bit quiet but more jokey like and open and we really had some great chemistry together.
We went doing different things with each other throughout the day.
We cuddled with each other a couple of times and we eventually had our first kiss that evening together. We held hands everywhere and soon enough she was actually talking about a full future together and making jokes about having babies and everything. We really clicked that day and it felt wonderful. By this time we were regularly talking on Facebook and we just were really really happy. We hung out again and we of course, had a lot of fun together and we ended the day by hanging out at the park. We sat in my car and made out together. She told me how much of a sweet sweet guy I was and she told me she sounded weird but when we kissed she said she felt like she felt something but didn't know if I felt anything. She also told me she was sorry she wasn't the prettiest girl out there but I told her to me she was. She told me she was really happy because of me and that made me in turn feel awesome During this time, we had a really attention **** girl that tried to be a third wheel on our relationship. I won't go into that whole story but basically she was trying to jump in and cause problems between us every chance. At first, me and my girlfriend agreed she would never come between us, and so it was for awhile. Eventually however, she got stressed out because the girl kept doing it and making even larger problems.
She eventually tried to take a break from me because of the overwhelming stress (this girl had caused her exes to try and get with her again, spread rumors and lies, and had people threaten her family even). She had had enough but I managed to convince her to stay with me and she said yes. She then said afterwards that I was an awesome boyfriend so she shouldn't let me go...The next couple of times we hung out, she was really quiet and kind of rude occasionally but still had her sweet moments and such, but it was a far cry from the happy goofy girl I'd met on new years. She also had the occasional mood swing and me being really good at psychology and such, I suspected she was bi-polar (I found out much later I was right) and she admitted she had OCD.
Anyways there was one time we hung out to where she was kind of in a mood, then we parked somewhere and she just busted into crying. She cried softly on my shoulder for awhile and I was there to comfort her. She then asked me later on if I ever felt like killing myself and she told me she did a lot, she also told me she had depression and struggled with life a lot because of her siblings and peers ruining it for her. Anyways, we went to our park again and she cried again but this time she was happy and she told me "You're such a good boyfriend" then she went on to say that this may not have been the longest she had but it was definitely the best. I felt awesome hearing that because I really did love her at that point and I felt so great that I was treating her right. We were really close, but then the girl who was starting stuff was at it again and bringing a lot of stress and annoyance to our relationship. Eventually, my girlfriend kind of got snappy with me one night and then I decided to give her some space throughout the day but then she messaged me saying it wasn't working, and that she had expected me to say something to her but didn't. After we talked, she told me she was still my girlfriend but she just wanted to take things slow so she could really understand my personality better (We hadn't been dating for even a month during this period) but she told me no one was going to steal her from me and that she was mine. I felt much better after that and went on.
Eventually the jealous girl did more crap and my girlfriend decided to hatch a plan to get rid of the girl once and for all. I was never told the entire plan but it consisted of her blocking me on Facebook and pretending like we broke up, then her pretending to be dating another guy and the plan would end with the annoying girl getting what was coming to her. I felt bad because she was fake dating someone else and on top of that, It was harder to talk to her because we always talked through Facebook and her phone was off, so she had to have wi-fi to talk to me and that was a struggle. Eventually we hung out and I felt tons better because she explained it better and we were still in love with each other. After awhile, I was talking to her via wi-fi one day and something came up with the third-wheel girl that I told her and she first off told me not to worry, but then she basically said "It's over" and didn't text me back until tomorrow but she then reassured it would only be temporary and that we just needed a break for all of it to blow over. However, about two days later, she was taking awhile to respond to my texts and I was already having a bad day and I asked if we could hang out, and four hours after no response, I went “...Or I could hang out with someone else” and she got mad and said “whatever” and I realized I messed up with that so I apologized and she told me to go f**k myself. Then the next 3 days, she tried to fully cut me off and she told me she didn’t want me to be a part of her life anymore and I felt terrible.
I then got an idea to bring her some donuts (her favorite food) and an apology card and leave it at her doorstep for her to find. Soon enough she did find it and sent me texts saying she was happy with it and she told me thank you and all of that. She said it was so sweet of me to do that all such. I felt good, but I should have been on my toes because the next two days after that she continued to dry or slow text me. It sucked that we were still disconnected but it was good we were talking again. Then I found out a week later that she was still trying to push me away and that the fake boyfriend she was “dating” she was actually dating for real this time. I felt terrible hearing that and I spent most of february in a rut. Soon, I got the idea to just confront her at her house, and so I did. She opened the door and she was shocked but not angry or anything. I told her a bit of my feelings and she was surprisingly open and funny with me again. She actually told me “Maybe” and smiled when I asked if we could date again and then she told me the guy she was dating barely talks to her so she didn't know what it really counted as, she gave me a hugs and told me it was nice to see me again.
I couldn't stay but I felt happy that me and her were for the most part cool. Since then, it has been more or less occasional texting conversations, but each conversation is kind of lifeless and disjointed. She broke up with the boyfriend after me and,I heard she misses her ex before me and she also wanted to date this guy much older than she was but said no to both because her ex and the older guy were known cheaters. The last time I talked to her, I tried to send her a nice text and she told me it wasn't cute (I do admit I messed up on it, I do overshoot boundaries and I was trying to soon to get her back) I apologize for that story being kind of long but I feel like I can't really leave much of this information out...I want in depth answers and some really good advice need help on this. I feel lost without her and I know deep down she may feel lost without me. I want to know how I should proceed with this, and I would also like any advice on what this girl's personality really is? I have a suspicion she also has borderline personality disorder but I'm not entirely sure.

She's admitted that she has OCD and you say that you "found out" she has bi-polar. At this point, I don't know why it's pertinent to know if she has borderline as we already have enough information to know that she's a troubled girl regardless of whether she's borderline or not. Why that particular diagnosis matters so much to you is a mystery to me.

From what I've read of your post, you both seem young and immature and it reads like she's playing the field. Now regarding what you should do.....I can't give you advice regarding that as the answer is one that can only be answered personally. I know what I'd do in your situation, but what's right for me may not be right for you. What advice would you give someone in the same situation as you with a supposed "girlfriend" who's playing the field, who's stringing you along with "false" breakups, who's being manipulative, etc.? That's where you'll get your answer.

You have a really good point on relying on self. I have my own plan for what to do in my head, I just like to hear different viewpoints from people and its hard sometimes to know what to do. I'll admit, the whole post could have been written better. It's just hard to really describe it in a way that really sounds educated (I wrote it kind of impulsively). My own plan I to keep on trying with it, I don't want to give up on it and I would love to help her in any way I can and be there. As for the Borderline, It was just simple curiousness.