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Susan, I've gone to a Chinese Restaurant in my area and spoken very carefully to the server about Celiac.  I was very fortunate that she had knowledge and experience with another patron.  I ordered steamed veggies W/shrimp and brown rice.  She made sure that only cornstarch was used on the shrimp - no flour!!  She also suggested adding garlic for flavor since the steamed dish is pretty bland without the sauce.  It's a huge step for me to be able to go out with my family for Chinese.  Maybe someday I'll research another dish.  Don't know about the drinks, but I used to love the scorpion bowls!!!  
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I love Chinese food and do eat at Chinese restaurants.  My first question is what brand soy sauce they use.  Most of them use Kikoman which contains gluten.  If they use a GF soy sauce, we're home free and just ask them to substitute rice noodles for any dish made with regular noodles, and to tell you if any items are breaded or floured.  Other than that, any dish with a white sauce is fine.  If they use a soy sauce with gluten, I ask them if they pre marinate their meat.  If they do, if they cannot use plain unmarinated meat, I just order vegetable dishes.  I bring my own soy sauce if they use one with gluten and add it after my dish has been cooked.  Some restaurants will actually cook with mine.  It sounds difficult, but once you learn which restaurants to go to, it is no big deal.  Good luck.  
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We eat in Chinese restaurants frequently.  As a celiac I have learned that Chinese food, for me, is the least dangerous form of restaurant eating.  I have gotten by successfully for several years now with now celiac symptoms and continuous negative follow-up testing. Generally, I have had absolutely no problems from eating egg drop soup, any white sauce preparations (which contain corn starch, not wheat flour).  I have had problems when eating at Chinese buffets and getting carried away with foods that I can successfully eat in restaurants.   Always check with the cook/waiters to see if they use cornstarch in their sauces.  Avoid most brown sauce foods as many soy sauces contain wheat.  I always bring my own soy sauce (La Choy) which is wheat free.
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There are things you can have in a Chinese restaurant. I always get a dish with a white sauce, typically this is something like chicken with snow peas or broccoli. I always say to the server I can't have soy sauce, what would they recommend. I don't even bother asking them if their soy sauce has wheat in it, I just avoid it. If it is possible I ask for MSG to be omitted as 
well. If not, I don't worry about it too much as MSG made in this country has no gluten in it. Always make sure the meat is not breaded or dipped in any flour.I do this and have had few problems.
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I have chow fun(chinese noodles) with pork or beef and bring my own soy sauce. Also have made up separately, veggies, rice and choice of chicken or pork or beef with WHITE SAUCE as it is made from corn starch and sometimes white wine. 
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Do be careful in Chinese restaurants. There is wheat in many, if not most. sauces used in Chinese cooking. My
partner is a gourmet cook and has been looking at recipes lately to see if she can do some gluten free Chinese cooking
for us and it's quite surprising the amount of wheat flour that is actually used in Chinese cooking. Good luck.
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I go from time to time with friends.  I order only plain steamed chicken and broccoli.  I remind them--no soy sauce (or you can bring your own) and I also bring my own Duck Sauce.  One restaurant offered to make me a plain white sauce but I have had some problems with restaurants--the person you speak to is often not the one cooking, pans are not always totally cleaned out, especially in Chinese restaurants where so many different things are being prepared at once and often there is a language problem.  I might trust one restaurant where I had a relationship with the owner, but I tend to be very careful since I have become quite ill after meals eaten out.My daughter, also a celiac, works in a steak/seafood restaurant and when she has a customer whom she knows is celiac, she stands over the chef/cook and makes sure they do it right.  They often want to take shortcuts---boil GF pasta in the regular pasta water (how much difference can it really make?) want to thicken things with flour--I'll just use a little bit, etc.  It's really foolish to trust getting sick to people who really don't understand the problem.  They are often just too busy to be as careful as we hope they will be.
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