It should be stated on the box if a power supply is included. It might differ from region to region.  Maybe you should contact Amazon with your concerns. 

Something else I noticed in my box is that there was no ac power adapter to plug in to a wall socket. From unbox videos I have seen there is one and also the manual says that it is included. Is this something new from fujifilm or did Amazon gave me a used camera sold as new? 

Probably. 

Hello, I recently got a new x-s20 from Amazon. I checked the shutter count using XApp and it says 163. Should the shutter count be zero in a new camera? Some people say that it might be testing at the factory. Is this true?

I never knew the X70 existed! Looks interesting.