Once you’ve installed Aurora Store it’s safest to disable automatic updates and then go to Blacklist Manager and blacklist any apps listed there that you have not installed yourself. This will ensure that no system apps are updated which could cause issues. Once you’ve done that you could re-enable automatic updates if you wish, my preference is always for manual updates.
I often see different apps listed for update in Aurora Store and App Lounge, although that’s not a real issue. They’re both pulling the information from the same source, the Play Store, and they do catch up with each other.
I also have a new FP6 and App Lounge is working OK for me at the moment. The advice is always to clear App Lounge cache and storage, reboot, then wait a few hours (up to 12) to try again. You’ll need to log back in again and reset preferences (auto update etc). A search in the forum for ‘App Lounge’ will show a number of recent posts with a similar issue, for example here: