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Tricky but doable.
China has a huge variety of food and I've traveled with vegetarians in China without much trouble. While all types of meat (and I mean ALL) are popular China, there are plenty of vegetarian foods as well.
Allergies are more difficult since the offending parts are harder to detect and the consequences of a misfire are more severe.
Some things to consider
I think with a few simple precautions this is manageable without too much trouble. The only exception would be if you have a severe raw soy allergy. This would require more comprehensive preparation.
Upvote:1
I have heard that vegetarian eating can be difficult in China. I read somewhere, long ago, that the best thing is to say you are Buddhist. Indeed, https://www.insiderjourneys.co.uk/blog/holidaying-in-china-for-vegetarians seems to back up that idea as well as providing other tips that sound worthwhile. However, its guide to what you can say doesn't include the phrase in Chinese characters - therefore you might struggle to make yourself understood unless you get the pronunciation and especially the tones correct.
As for your nut allergies, sorry, but I can't help you there.
Upvote:1
Vegetarian is tricky in China, but doable. A small selection of restaurants cater to Buddhists who do not eat meat (and are, in fact, vegan).
The real headache is your peanut allergy, though. It is very common for Chinese restaurants to cook with peanut oil, so if your tolerance is low enough, then tough luck. But fortunately, there are also restaurants which use rapeseed, soybean or corn oil (those are the most common cooking oils in China). Of course, it doesn't hurt to ask (it would greatly help if you go with someone who could explain it to the waiters), but expect a lot of the restaurants to use peanut oil.
Also, I'm not sure what "raw soy allergy" means: do people actually eat raw soybeans? (They contain lectins and I thought they can't be eaten raw anyways.) If that means you're allergic to soy sauce, then even tougher luck...
There are some salad restaurants in Beijing, though. I'd be pretty sure you'd be fine with those...