Iphone 8 App Store Not Working No Fixes Have Helped
I had the same issue with my new iPhone 8 Plus. I came from an iPhone 7 and never had that issue, although it seems relates to the Apple ID.

What i did to temporaly work around it was to shut down the phone and turn it on again. Now i was able to download and update apps again.

Also you can try to reset your keychain.

Settings > [Your name]  > iCloud > Keychain

Also, try updating to iOS 11.0.3 
At the time i had the issue i was with iOS 11.0.1