Him Berbert, the train ticket from Xian to Beijing costs 400/417RMB per person for a soft sleeper. You should pay service charge if you buy in advance. The fatest train will take 11 hours. It is 2 hours by air and the 50 percent discount off air tickets which costs 90USD including airport tax is available if booking now. I recomment you check the information on China trains(https://www.travelchinaguide.com/china-trains/) and latest price of China flights(https://www.travelchinaguide.com/china-flights/) just in this site. Travelchinaguide provide details and reliable informations on these. Four days are quite enough to finish these attractions and you can even add some more, these can be done in three days at most. Travelchinaguide, this china tour(https://www.travelchinaguide.com/tour/default.htm) operator will help you arrange a guided tour. You can make inquiry about the price. I has been very cold here in Xian and Beijing. Keep warm.