Wen, the traditional cuisine depends highly on the region, so which authentic Chinese dinner we'd have depends on which restaurant catering to the local Chinese population we go to. I cook it some at home, and the cookbook is widely regarded, but it mixes all the cuisines together and doesn't give much information on menu construction or how things are served.
I know well about the tones, the bane of my college Mandarin classes! But Cantonese, I hear, is even harder. LOL, seeing it written out brings back memories, I even went to one of the immersion course camps in Minnesota. But today my Chinese is like my German: I'm lucky if I can order ice cream in it!
I hope to do better with the girls for languages. We're now studying French and German as a family, and classical Greek and Latin, but that's not really something you converse in.