Intercultural communication

I was not here for the intercultural communication lesson, so I will tell and example of a personal cross cultural miscommunication.

Once when I was studying at a Chinese university, a young woman approached me in the library study room and we started talking. In the conversation, she had lavished praise that seemed a tad excessive. I misinterpreted this as an effort to flirt. She seemed friendly, and I figured that her type of approach was tantamount to an ask-out in China. As-per my policy of giving anyone who gathers the courage to ask someone out two dates/meetings, I asked her out. I was wrong. When I asked her out, in a respectful manner, she was flat-out shocked, and seemed a little offended or embarrassed. When I recounted the situation to my American friends, they were equally confused.

In a different situation and with a different girl, I merely asked if she wanted to meet at the cafeteria to eat dinner together. My thinking was, 'we all have to eat, and if we’re going to eat at the cafeteria, might as well eat together.' In the US, this does not constitute a date, but is rather in the grey area between date and just hanging out – it is not a date but could lead to a date. Well, this sweet young woman came decked out in a beautiful silk dress and makeup. I felt like a jerk. I was embarrassing her because I had not worn anything that special, just a standard polo shirt (I was thankful I had not donned a tshirt that morning). I was afraid that this miscommunication would be obvious to other students. I considered suggesting that we go to a nearby restaurant instead, but didn't as I thought it would tell her that I wanted to date. I have been told that it is normal for women to dress much better than men in these situations, and that I should not worry about it. Is that true? Should I have switched plans and offered to take her to a restaurant instead?