I will arrive Hangzhou about 2200hrs, which is the best and fastest way travel to Beijing.

Taking flight from Hangzhou to Beijing is of course the fastest way. There is also direct train from Hangzhou to Beijing, but it takes a long time. Since you will arrive Hangzhou so late, you'd better stay in Hangzhou for one night and go to Beijing the next day. You can take bullet train from Hangzhou to Shanghai Hongqiao railway station and then take bullet train from Shanghai to Beijing. Both of the two train stations in Beijing are far from the Great Wall. March is the end of winter time in Beijing. It is still cold. You need to prepare warm clothes.