I think you will find answers for pretty much all your questions on the forum already.
You have to reinstall google apps after EVERY update. It’s in the instructions as documented here
If the updater app says you are running Android 4.2.2 and doesn’t saying you’re running Fairphone OS vx.x then it sounds like you’ve installed the standard android (AOSP) install rather than the Fairphone customisation. If you don’t have the Advanced button at the bottom of the app, you will probably have to reinstall the Fairphone OS version manually as documented in this guide. This topic is a good one to read
If your phone is saying it is roaming all the time this is probably linked to the above. You’ll need to install Fairphone OS. I would recommend v1.6 as there are problems with v1.8
Yes, there have been problems with testing and these are being address by the Fairphone team. They are hoping that the next version (which we’re expecting to be something like v1.8.1) will go through a proper beta test. This topic is relevant for you to read.