Hi Joel,
How do you edit or organize folders? Do these buttons become grey out? You can share the steps here so that we can do more research.
In Outlook 2016 for Mac, we can click Home tab > New Items button and then choose “Folder at This Level” or “Folder” to add folders. Besides, we cannot rename Inbox.

>>I also am unable to drag messaged from my inbox to move them into the folders.
I now can only control/click on messages to use the drop down menu to move them.
If you right click the message, can you use the Move option to move messages? Does issue only occur when you drag and drop?
We can
create a new profile to test the result.
Besides, what’s the detailed version of Outlook for Mac? Please upgrade Office to the newest version to see if it helps.
Any updates, please feel free to post back.
Regards,
Perry
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