All of a sudden (without any known change to my PC or its drives other than coming out of hibernation) I got a box entitled "Give DropBox permission) asking me to give Dropbox permission to my DropBox folder. Why? Is this legitimate?
Sounds like Dropbox has done an update to the software and is just setting things back up - possibly moving to the new Cloud location structure. Yes these are legitimate messages so just approve
It's also important to check what type of permission is being requested! I mean "Permission to do what, or handle what?" But if it's simply permission for access, that's okay, especially if you're working on the cloud across different devices, and Dropbox needs to put everything in sync!