I think you need 2 separate tickets for your journey, as in China they have local reservation system at each big station.
In Beijing should be no problem to buy a ticket as they have ticket desks for foreigners.
There are 4 types of carriages in China.
1. Soft or Hard Seat Carriage
2. 6 berth sleeper compartment
3. 4 berth sleeper compartment
4. 2 berth sleeper compartment
Here's good source for all Chinese trains between major cities
http://www.cnvol.com/