I think the only part we can pick as being racist are the major instances mentioned already where she tried to invalidate OP as being a 'real' Chinese because she adopted or being some bratty kid for saying she's more Asian than OP (not sure when it became a competition to this chick). The other things are really just a combination of ignorance, immaturity, over enthusiasm, and ego problems from how I see them, they don't even fall into the micro-aggression theory of racism. OP's shitty [soon to be hopefully, ex-] friend isn't some raging racist that goes around and falls into "the belief that all members of each race possess characteristics or abilities specific to that race, especially so as to distinguish it as inferior or superior to another race or races." She's not saying OP's race is inferior by being bad at speaking the language (I took 3 years of Chinese in high school, teacher being a native from China, and it's an INCREDIBLY DIFFICULT language, a wonderful one, truly I really love learning about it, but I have no good sense of how to handle tones still, so I highly doubt her friend does either especially without formal training), or that all Asians in general are inferior, she definitely isn't looking down on the culture, but she is being horribly ignorant in the teenager kind of way by trying to invalidate OP to make herself some sort of poster-child.

Maybe I just don't see it because I'm white, but I've experienced the extreme racists and I just see those as being the true problem, while many other issues are just annoyances. I'll be honest, I had an ex-boyfriend (he's an ex for this reason, and was my top reason for dumping him, though I had others) who was racists against both blacks and Asians, and it was awful to be around it got to a point I felt ashamed of myself for having interest in cultures that weren't my own and for having FRIENDS of varying races. Like how dare I have 'friends that were inferior to our race (actually he was half-white, half-minority)', like he didn't even see them for being the wonderful people they were or the deep culture that it was. Honestly, I feel pity for him if anything, he's actually dating an Asian right now (he's never once called her attractive), and I hope she never talks about her culture to him while they date so he doesn't beat her down. Maybe she'll change him, but from when I knew him Asians, especially Chinese actually, and blacks were just shitty people in his mind based only on their skin color. He has painted my picture for what I think racism is and he's not even the worst that I've run into, so it's hard to just throw this girl into the same circle as him. OP's 'friend' is definitely a shitty person in my opinion, she's stupid and ignorant, and I hope she eventually keeps an interest in the culture that her misconceptions clear up in the future, but that definitely doesn't give her a pass to hate on OP because she's jealous of her skin color.