I am wondering about a woman she goes to extreme emotions with me, sweet to angry?

I feel like I have some kind of affect on her, she does have an affect on me as well. But I am confused as hell with her. I do not know what she wants.
From the moment we met she could not get her eyes off me, we spent two years around each other mutual friends and every single time I would catch her looking at me. Sometimes she would stare me in the eyes while she is talking to others as well not only me. Whenever she sees me she would want to tell me about her day and what she did. She opened up to our group about her two failed marriages and she was so embarrassed about it and how she thinks that her current bf will leave her too.
We have an age gap and she has a daughter my age and she keeps telling me how she is older than me and that I am he daughters age. ( I am not young im in my late 20s)
Sometimes she seems like she does not know what to do or how to feel she act extermly caring and flirting, then the other days she would act angry and snap at the smallest things. I do not know why I attract those strong emotional reactions from her. She is so calm with our other friends. I never seen her losing her cool with them. But anything I do even without intention would piss her off.
I had my papers thrown at the table, a chair pushed at me, got yelled at few times.
Then on the other hand she would act caring way too much. She can know how I feel just by looking at me, she says she misses me when I am not around, she gets worried about me when there is a storm or something like that. She always tell me to get home safe. She almost cried multiples times when I went through tough things in life and hugged me to calm me down and tried to help me even without me asking, she helped me a lot. she defended me many times and acted so protective over me. I had some friends telling me that she cares about me and even loves me ( they did not mean real love). many times tried to teas me talking about kissing. One time I gave her a simple gift and she said she felt like crying.
She asked me once to hang out alone and I panicked because I did not know what to expect.
She always reply to my text. But she never text first, but in real life she would make up and excuse to talk with me.
We parted ways for an year and I was thinking to send her a text happy birthday. But I do not want to do it until I understand what the hell is going in this connection. Can someone give me some input?