We arrive Shanghai, but then train to Beijing for 3 day tour, do we register free transit visa?

Jen, the 72 hour free transit is not applicable to your situation because 72 hour policy is only applicable to those traveling by flight and you are only allowed to transit in one Chinese city. Considering your situation, you should apply for a tourist L type for your trip. Of course, a transit G type can also work if you won’t fly back to the country you flied from, but a third country or region.