Good day! Please tell me if there is a train Nanning - Hanoi, and what his schedule and cost.

The direct trainfrom NN to Hanoi exists and it starts at around 18:20 from NN and reach Hanoi at around 04:00 the next day.
The fare is around 300RMB for the hard sleeper and 220RMB for the soft sleeper.

One more question, if I may ... Is there a train Beijing - Hanoi, what his schedule, cost. Please advise which route is best to get from Beijing to Hanoi. Thanks in advance.

Yes, there is train service from Beijing to Hanoi. It only operates on Thursdays and Sundays, leaving from Beijing West Train Station at 15:45. I remember the train ticket fare is 2,354RMB per person for a soft sleeper. And there are only soft sleepers on the train.
Apart from the train, you can also fly from Beijing directly to Hanoi.