If you are thinking about using the airport bus early in the morning, you need to go to Nanjiang Hotel on Dongfeng West Rd (near Wal-Mart on Renmin Lu). It is the only airport bus start running early in the morning. The airport bus start running around 6am (every 20min). The airport bus at Beichen start at 8am. Your best bet is to take the local bus (no. 61) to Wal-Mart on Renmin Lu and walk to Nanjiang Hotel (5min). No.61 start running at 6am (from the north) and it will get to northern train station stop in 15-20min. Or you can take a cab to Nanjiang Hotel, it will cost you around 12-15rmb from northern train station. I just came back from my trip to the states and I lived on Beijing Lu near northern train station. Good luck to you!
Yes, Jan 1-3 are days off in China, but some private language schools (like my school) still operating during those days.
In regard to Chinese New Year in 2011, it is on Feb 3. Some Chinese start their holiday one week before. It is normal thing in China, the schools (or staffs) do not know of their schedule for the holidays until it is 1-2 months before the holiday (if you are lucky enough, sometime they let you know a week before). They do not plan ahead, like most western countries with their holidays schedule. If you are planning for a getaway or vacation during the Chinese New Year, I suggest you just make your plan and then, let your school know you will not be available during those days (between middle of Jan to middle of Feb). Don't wait for the school to tell you about the holiday schedule, unless you just plan to just stay in town.