From Beijing West station, can we book trains departing any route in China?

Me and my boyfriend land in Beijing on May 22nd. We want to book hard sleeper berths from beijing-qufu on May 25th. Is this enough time to reserve tickets at the Beijing West station? Also, at the Beijing West station can we reserve tickets for train travel over the next two weeks, departing from Yanzhou (near qufu) - Shanghai, Shanghai - Nanjing, Nanjing - Xian? Finally, we want to travel to Lhasa from Xian on June 8th for a tour in Lhasa starting June 9th. We want to arrive Xian on June 4th. Is it a good idea to wait and book sleeper berths in Xian? Will this be enough time? The online booking agencies are very expensive... Thank you so much! Shannon