FIeld Report: What does she do and want


I'm struggling with some situations. I met a girl at my work. She's made a compliment to me and meant that I would be handsome and had the same stature like a buddy of hers.
Then later, we went to break, went to some shops to eat something. She asked me where to go now and what to do. We went on. Once, she saw some guys eating outside and wished them a nice meal while she went next to me. I didn't understand what this should be.
Then finally I went in a bakery. She followed me. There we ordered something. While ordering the cashier wondered about us and that girl said she wouldn't know me. I told her that this didn't sound different the day before. Later She told there cashier that she was just fooling me. When I asked her if she spoke my language, she turned it around and asked the cashier if it had something to do with her language. In the beginning I tried to explain but later i gave up and let her talk. The cashier didn't react any more to me. After paying, we went. This time she was in front of me, but another female customer looked angrily at me.
Later I spoke to her that she would be a stranger and she giggled but was just self confident. No more shit tests or negs.
Later in office, she negged me. I made the experience that she makes a scene when there are other people present.

I don't know how to deal with that. Is she shit testing me or just playing around to increase her own value?

A day later she was pissed. When I said something to her cause I felt sry for her, she was walking away and said:
"NO, you are down through at me."
Then she walked away, turned her around and said "I'm sorry but that's my rule".
Later she tried to lower my value in my absence cause other coworkers started testing me. One even reminded me to take my stuff with me before leaving.

Those are too many signals and meaning that I can't figure out all of them. Should I ditch and behave like a man by ignoring her? Or teasing her?