Since this is your second meeting, it's possible she did truly just lose track of time and was very sorry. However, you don't know each other that well yet so don't be put out if she was attempting to politely suggest you leave. As you get to know each other, you may become friends, but dont expect to be great friends straight away

I'm not quite sure what you mean by going to her office. Does she work on the college campus? I wouldn't say it was impolite to go, but I perhaps wouldn't have done it. If she is still staying in college accomodation or a place she was renting, it's very common for housing to be on or very near campus.

Err to be honest, I think you just sound a little nervous/paranoid. She sounds nice

I recently knew an American girl she had just graduated from a famous college.I am a Taiwanese girl and we have language exchange.We have appointment every friday from 2:00~3:00.Today is our second times,she was late for half hour.So I asked someone where was her office and I came to her office to find her.
1.is it polite to go to her office directly?did I offend her privacy? but I am not sure if I should keep waiting.Her door was locked and I knocked the door and she welcomed me and apologized several times and told me she was too busy to remember. Is it her excuse because she is not interested in making friends with me?
2.She was chatting on the MSN and her collegues came in and she introduced me like " hey this is my friend,she found me,I forgot our appointment" and I feel that she just tried to be polite and it doesn`t mean anything.
3.She talked to me for a while very friendly and she told me today is her birthday and she invited me to her house and I shouted "you have a house on the campus? so cool" and I noticed her american colleague looked at me for a while. Is it polite to say that?
4.After a while about 3:00 she kept telling me that next week she would remember.This make me feel she implied me to leave and as the moment I stood up she said good bye immediately.Was she really interested in talking to me? During our conversation she continued chatting on MSN.
Is it appropriate to talk to her in her office?
5. Do you think she want to make friends with me? or she doesn`t care about me and she just to be polite?