lucydawlish,
Have you read the trouble shooting articles on the support page which explains how to move and delete folders. Note that on a WordPress site images are often embedded on posts and pages. When a users moves or renames a folder, then that could break the links to images in posts or page. Thus if you want to move a folder or rename a folder, create a new folder then move the files to the new folder. When file are moved, then Media Library Folders updates their links in standard WordPress posts and pages. And to delete a folder, you need to first delete all the files in the folder then you can delete the folder. The purpose of this is to prevent the accidental deleting of important files.