Are railway tickets cheaper for children? Is there a price difference when you buy roundtrip ticket?

Yes. In china, kids lower than 120cm could take train for free, however, who will have to share the seat/berth with his/her parent. Children between 120cm and 150cm in height could buy child ticket with seat/berth.
For round trip tickets, if the type of trains are the same, the price is the same for the same seat class.