You're correct, the improperly formatted drive is the most likely the culprit for the errors. FAT/FAT32 are the required formatting types for the Rekordbox system when using an external drive.
To be honest, I'm not entirely sure the proper course for you take with regards to solving the problem. In theory, you could purchase a new external drive, format it properly and then copy/paste the contents from the old drive to the new drive. There's a chance that it may not work if there are some hidden folder/files required by the Rekordbox system.
On your laptop, do you still have a copy of all your analyzed music? If so, perhaps you can try performing an Export from Rekordbox to a new drive (non-partitioned, properly formatted). Then set that drive as the new Database.
These are just a couple ideas off the top of my head. @Pulse or @Mark may be able to recommend a better approach.