About the screen, it may be hardware-related: take off the screen, clean the connectors and put it back. It is often as simple as that and it’s always the first thing to try.
To check if you have the correct OS, just open the updater app and check what it says (“Your current operating system version” --> Fairphone OS or Fairphone Open?).
Once you’ll done all the installation, you’ll be happy with your phone. And if Fairphone Open seems too complicated to install/configure, ask a Fairphone Angel, a community near you or go back to Fairphone OS. With the regular Fairphone OS, the phone will work just like other Android phones. With Fairphone open, it should work even better 
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