That's a little too wishful of a statement, freedom is guaranteed of course, but there is no rule that free software will be more private just by virtue of having its code be open. For instance many free apps will still include analytics (proprietary or not), it's not the case with this one luckily
Yes! Turn off automatic updates for the Voyager app in Play Store. Then just update the Voyager app like normal through F-droid (F-droid should automatically recognize Voyager is installed)
Unless the app allows you to export/import your settings, unfortunately the answer is no.
This is because F-Droid builds its own installers and signs them with their own key. Android (sensibly) does not allow upgrading a package if the signing key is not the same.
Actually, Voyager has reproducible builds enabled. This means F-droid distributes the app with the same key that is used for everywhere else Voyager is distributed (Github releases, Play store).
So if you want to migrate from Play Store to F-droid, turn off automatic updates for Voyager in Play Store and update the app with F-droid :)