I see from the screen shots that it's possible to make nested folders, but how does a user do it from the web interface? I don't see a spot to indentify the parent folder if any.
To make one you Parent Folder.Sup-Folder but it may be different depending on your mail sever.
I'm using Dreamhost. Can it be done through the webmail interface?
Yes Dreamhost can do it, just go to settings-folders-New folder-Folder.Sup-Folder