LOL! tbh, (though this may very likely offend most westernized, non-country bumpkin chinese), there's still a case of widespread 'white-superiority' complex in east asian countries. it is especially so in china. i've heard so many cases of gorgeous and successful chinese girls dating ugly, penniless white guys just because they are white. it's sad, but i'd guess it's about wanting one of those adorable eurasian babies, and wanting to try something out of the norm.
异国恋情 (loosely translates to "foreign love" or rather "finding love abroad") is what it's called in the context of the girl being physically in a foreign land.
To answer your questions, in the chinese culture, the girls are taught to wait for the guy to make the first move. So you either ask her out, or watch some other guy get to her first. She ain't gon do nothin' even if the world were to end tomorrow. It's a sign of lack of self-respect. secondly, physical intimacy is a huge issue. even hand holding is a major, major relationship milestone. '男女授受不亲' (google translate it yo'self) Don't you even dare try touch the poor girl unless you're keen on a serious relationship. Lastly, there's no time bar as to when to ask her out, but the first date should preferably be a traditional to semi-traditional one, going to the movies and what not, to show immense respect and sincerity.
Everything else is pretty much the same. But with the rapid expansion of china's economy, globalisation and all that jazz these days, there aren't many chinese girls who stick to such a traditional mindset anymore.
white, brown, black, yellow, we're all pretty human.
you're probably over-analysing the race factor.
Look past it and get to know her as a Woman, a Unique Individual; not a Chinese (with the capital C) girl.