Buying train tickets on route

During our trip we will be using trains pretty often.
Is it possible on train stations of train ticket offices to buy traintickets for further our trip?
Can we buy in train ticket office on airport our traintickets from: Beijing to Pingyao, from Pingyao to Xian and from Xian to Chengdu. And later on in Chengdu buijng our traintickets from Lijiang to Dali/Dali to Guilin/Gulin to Shenzhen?