Hi, glad i could help. Generally there aren't that many days when the pollution is dire, January this year was very unique in the fact that i think about half of the days were awful whereas normaly you would probably just get a handful of bad days. At this time of the year it is because of the run up to Chinese New Year and the factories are on overdrive before shutting down for a week. Also because it's really cold everyone has their fires going! This isn't to say that on the other days that the air is fine, there is still a lot of pollution compared to the UK but you kind of get used to it and even when the the air quality index reads 160, for example, you do think 'ooh that isn't bad'! (anything over 100 in the UK would be a national crisis)!! The average daily reading, i would say, is between 100 - 200. You tend not to notice it too because when you look outside it doesn't look too bad at these readings and most of the time it is sunny here, even in the winter so that is really nice. If you have a grey day it's usually down to the air quality lol! Shunyi is generally the same as downtown. As Shanghaidiva has said you can get masks but they are a waste of time really. We just don't go out if we're at home on really bad days and at school, the children also don't get outdoor play. Air purifiers in the home would be a better investment.
When you come out for your look-see, if you are not sure on whether you want to live downtown or Shunyi, then i would have a look at both, although it will depend on how long you will have out here. Have a think about what curriculum you want your children to follow, eg English national curriculum or other , this link here should be very helpful in giving you an insight to what's available (there is a lot of choice!) www.beijing-kids.com/beijingkids-School-Guide and then look for housing compounds close to the school of your choice - Beijing is HUGE and what may seem like close by on a map could take a long time to get to particularly at rush hour times. Other than that, go out and get a feel of the city, check out some of the expat supermarkets - either 'Jenny's' or 'Jenny Wang's' , a shopping centre like Solana, Sanlitun an area of downtown is lovely and has some great restaurants and bars (although some not so great at night time iykwim) and shops and I always think the city has an amazing feel at night (not that i go out that often!).
You can transfer money but not sure of the amount, 20K seems a bit high to me from what i can remember, but i'm not an expert as we're paid in the GBP.
Re. nuts, I knew a lady here with a son who was extremely allergic to nuts and they had to be VERY careful but generally they were fine and as far as i am aware they did eat out. You would have to make sure you go to restaurants that cater for Westerners and that can speak English so that you can communicate your wishes. You will need to make sure you carry an epi pen with you at all times just in case but as a reassurance there are some very good hospitals and medical clinics here. Oh and also you will need to bring spare epi pens with you too as they are not available at all in China as there is no license for them.
Sorry for another essay, hope this is of use. Let me know when you're over on your look-see flowerpowergirl.