If you are on the dining plan and want to use a counter service meal, Disney doesn't differentiate between childrens and adult meals in the allotment, they are all just listed as QS meals. There are some QS locations where there wasn't a choice that my DD liked the kids options so I just ordered her an adult meal. It didn't happen often, there were just a couple of places. Also some QS locations don't have kids meals and so they would order a meal just like an adult.
Nothing listed on the menu. You could pay OOP or share a meal. If you are on the meal plan, you can order the meal and just use the credit. They don't differentiate between kids credits and adults.
My DD11 loves Chinese food too and the Yak & Yeti counter service was very good. We just order one thing of the beef lo mein, one chicken fried rice and a couple of egg rolls and it was plenty to share.