I live in China, almost 10 years now. End of September is a good time, better than average chance of getting good air quality. As some have said, if it's a real concern buy the 3M masks. For a short term stay I suspect the body can handle it without any long term effects. Visine is helpful for many as well. If you live here you get used to it, the price you pay to be part of a very vibrant country.
As for Beijing, go to Jingshan Park before going to the Forbidden City, you can walk down the hill from the park to the North entrance. Also, go to the street food market in Wangfujing at night, great experience. Take the Subway whenever you can, Beijing traffic can be exceptionally bad and it's easy to use the Subway here. Try to keep your schedule flexible, that is you want to be at the Great Wall when the air is clearest for a better experience. The hotel can arrange a driver on short notice to take you there, so if you wake up and it's clear, go.