Beijing and Lhasa - Train / accommodation

Hello travellers

Who can help me with train and accommodation information as follows:

I would like to go by train to Lhasa. Does anybody know , is it a problem to get a train ticket (hard sleeper) from Xining to Lhasa?

Also I would be thankful for an address from a central, clean and very reasonable hostel in Beijing and in Lhasa.

Thank you for your help.

Greetings - Countrycow :-)
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