Fairphone does not automatically connect to cellphone network (and other issues)

I see your point with the Google Play issue but remember that the phone does run android, which is pretty much Google’s OS. There’s a lot of talk on here about alternatives. So if a user is interested in the information it may not be on the phone itself, but it is available on the website and the forum here.

The whole settings bug is very weird, I understand now what you were trying to say.
The next idea I can think of is checking which Fairphone version you have installed in the Fairphone Updater app and upgrading to 1.6, if that’s not already installed.
Another idea would be flashing the OS to your phone in recovery mode (OS-files are here / please also read here!).

Other than that I’m at a loss.

I’d recommend raising a ticket with Support. You may have to wait a few days but you can get help from the source. Also I think it’d be a good idea to report this bug to them.