How do we go to Badaling from the airport? We are arriving past 12 midnight of April 15, 2013.

I'm afraid no public transport can take you to Badaling at that time. You'd better stay in nearby hotel overnight and head for Badaling on the nest day.
Well, from the airport, you can take the Airport Express Train to Dongzhimen first. Then take subway line 2 to Jishuitan, where you can transfer to bus no. 919 to Badaling Great Wall.