Short version:
-No skills with woman
-shy and at the same time sociable
-relationship:1.4years
-broke up
-got back together
-broke up again
-she sends me iois one day, another day it's just not like that
-I want to get back together
*more details in Long story*
What do I do?

Long Story:
Hi, just to mention I have absolutely no experience with girls, the only thing is that I had a girlfriend for a year and a month untill some douche (a year and a half ago) took advantage off her ( bipolar disorder, so she was at her weakest back then) and took her away, we decided to stay friends. After a week she asked me if I was content this way.
As stupid as I was, I said yes ( because she seemed like she was happy and I didn't want to ruin her happyness) after a week, I really wanted her back, so I told her, and she was together with that douche ( didn't know it from the day we broke up, hardest part is that is was a good friend), so she started making excuses like no my psychiatrist said I need to stick to my decisions, etc. After a few weeks she found a gun in her room from that guy, so she broke up because that was disrepectfull to her that she didn't know it. and after talking about the whole situation she gave me back a chance.
Unfortunatly, I ruined that chance. few weeks later, again a chance, but then on New Year, She was extremely drunk, and she kissed with another dude( again a friend off mine) and then passed out, I have been looking out for her the whole night including some other nights when she passed out. But nobody told me she kissed that guy. So when I found out, I decided to part ways as a friend, because I didn't get the respect I deserve and she lied to me more than someone would ever do.
Nowadays, we are friends again, She helped me ,while nobody wanted to help me, when I was passed out on her birthday ( we were @ the same Youthcafe, because there were playing some awesome bands). This gig was I guess 6 months ago. Since then, we are almost always one evening in a week together.
Since then, I'm really confused, one evening she gives me the iois and the other night she doesn't. last wednesday, we went to the youthcafe again and we were talking, and she was changing her looks between my eyes and mouth ( not sure if this means something, could've had been bad breath or something), always if there's a song playing like "A day to remember- if it means a lot to you" She always starts singing and looks me right in the eyes when she sings. And then other days, she isn't that much talkable and she gives me emotionless and short answers.
Also when she has a boyfriend or has gone on a date and they come to the same pub as I am ( as she always does) She suddenly ignores her boyfriend or her date and comes sit next to me. Small fact: She smokes, I smoke. When she wants to smoke she doens't ask her boyfriend or date ( that also smokes) to go smoking, She only looks at me, and asks me if I want to go smoke. and talks mostly of the time only to me.

I'm really confused, what should I do? I don't have much girly friends to make her jeaulous or any type of things... . I'm really social but really shy, so I don't meet alot of people.

another fact: a few weeks ago she told me she had a date with a guy, so I was (again) dissapointed in myself that it wasn't me. So she noticed that I wasn't that happy, and she started talking about what's the matter, what she did wrong and stuff ( I'm not really a guy who likes to tell about myself and how I feel and stuff, I just don't, I just crop it up, and move further withouth talking) but when she said: your upset for my date, aren't you?, so i said: "yes, I wished it was me." Don't know what she answered back then, because I was a bit drunk and she was too, but I remember her saying the same evening:" I would never want to have a fight with you, you are together with my mom, the most important person in my life".

- and I'm quite sure she cheated on me the last night we where together, Because she said on the last minute she couldn't go to the party with me because she was 'sick' but when I got to her home to surprise her before the party, that douche was standing there, and she looked healthy enough for a party, untill she saw me, she was happy to see me, but suddenly acted sick-

Also one big problem: she doens't take me serious.

what can I do? I don't want to give this all up, because we know each other like no one else does, and I don't want to think about the thought about giving up without trying my hardest and everything I could.

again:what should I do? I guess I've explained almost every litle detail I can think off, just to be sure it's clearly!

Stay away from her. Do you think so little of yourself that you'd be willing to give this girl a second chance (or is it third? fourth? I lost track in the story) after she left you for someone else, cheated on you, and is clearly mindfucking you for no reason other than to get your attention? She's an attention whore and is giving you mixed signals so that you'll pine over her and that is what gives her validation.

Your thought process is normal for someone who has only been in one relationship before, but it's important to go out and meet new people. Imagine if you had some other girl on the sideline who is just as pretty, smart, funny, and understanding as your ex. Or what if she was even better? You wouldn't give a shit about your ex anymore, would you?

As for your lack of skills with women: for now, focus on not improving your skills with women, but improving your skills with talking to people in general and being a fun, social guy. At that point, your skills with women will develop naturally.