Buying train tickets at Bejing train station

We are in China from September 3 to September 12. We need train tickets for 2 journeys: First, we want to go from Bejing to Taiyuan on a fast train and transfer to a regular train to go to Pingyao on September 6. Second: on September 12 we want to go from Changsha to Shenzhen on a fast train in the afternoon (assuming our bus from Fenghuang leaving at 830am is on time to Changsha). Can I buy both tickets from the Beijing ticket office on September 3? Or do I have to buy the Changsha tickets in Changsha only? If I use the travelchinaguide.com pre-sale booking, are the prices for the tickets the same as if I bought them at the ticket office? For these 2 journeys, can my hotel make the purchase or do I have to do it myself with my Identification?