Buy train ticket from shanghai to beijing or other big city likes as Xian, Chongqing, Guangzhou

My wife and I will arrive at Pudong airport early in the morning 4am at 12/9/2018. Is it possible to use line 2 metro subway from pudong direct to nanjing east station? And if We want to travel from Shanghai to Beijing, is it possible if we buy ticket at the day we will travelling (17/9/2018) or must spare 2-3 days before? Or must we arrange it 1 month before by online? Thank you