I lived in China for a year (but not in Beijing). I've spent about a week total in Beijing though. I was childless at the time, and I didn't have a cellphone, but I'd be happy to answer any general living in China Qs.
Re: your Qs, I'm definitely pro-Subway, and pro-avoiding rushhour (w/ a baby). And I think the air purifier is a good idea. A couple of years ago, I did a two week trip that was Hong Kong, Guangzhou, Shanghai, Beijing. I was hoarse from the day I entered Guangzhou til the day I got back to the US.
I'd also recommend getting outside of Beijing on the weekend (or whenever you can). My experience in China is that the countryside is quite beautiful / pleasant to be in. When I was in Beijing, I went on a tour with this group:
http://chinaculturecenter.org/ It was great! The guide was really good, and there was no touristy / sales element to it at all. We were on a minibus, and I'm not sure if they offer carseats. It does look like they have some kid-specific tours, though.
If you want to bring a carseat with you, we use the Cosco Scenera as a travel carseat and it has been great. It's light and easy to install.
Also, if you don't already, I'd recommend looking into babywearing. It's a great way to carry your kid in places with a lot of walking (and crowds) and public transportation. There are all sorts of options. When our daughter was little, my wife really liked slings / wraps, but I've preferred using a soft-structured carrier like an ergo or a lille baby.