If there are 8 tapes in rotation, each replaced ONLY after the previous one is full, does the replacement still need to have an inventory job run on it regardless if it is new or old?
Yes. Inventory is the only way to tell BackupExec that the media has been changed in a stand-alone drive. (If you have a library/loader and have enabled bar-codes you can run a scan rather than an inventor)
Does the overwrite protection need to be removed on all old tapes so the backup can be done when it comes up in the rotation?
If OPP and APP are managed properly, you should not need to do anything to reuse tapes.
With the protection set to 'infinite' wouldn't it be impossible to overwrite a tape coming up in the rotation even if it hasn't been used for say 6-8 weeks?
Yes, with OPP set to infinite, you would never be able to overwrite a tape without intervention
Since we never performed an actual inventory, would it better to take all the tapes, erase them, re-inventory and recreate the media labels and start over?
You will probably have to, since Backup Exec has probabluy written the same media id to each tape.
You may be able to get data off those tapes by shutting down all BackupExec services, renaming the \Catalogs directory to catalogs.save and then restarting the services. A new \catalogs directory should be created. then try the inventory and catalog again