We travel from Bangkok to Shanghai and after 6 days to Amsterdam. Can we stay without visa?

If those are all your stops within the itinerary, you are definitely eligible for 144 hours visa free transit in Shanghai. Yes, you can stay in Shanghai without visa. That is the purpose of this transit scheme :)

Van we use the bullet train to
Hangzhou for 1 day out of Shanghai also?

Of course, you can. You can travel within the entire zone of Shanghai City and the provinces of Zhejiang and Jiangsu with any mean of available transport. You are literally free to travel, to visit and to stay in every corner of this part of China within the mentioned time frame.

Thank you Zupan for the information given