Thank you for your feedback, regarding the questions:
1 a). Unlabeled attachments won't appear into "Labels" folder instead you can find such attachments under "Contacts" into specific sub-folder (represented by sender's email address).
1 b). Attachments with multiple labels will list into each associated label folder under main "Labels" folder. This means same attachment will be listed multiple times in each folder.
2). Moving files from "Gmail" storange link folder into newly created sub-directories will put all of such files into "Not allowed" list in odrive tray menu. Well, changes made from desktop in Gmail storage link folder will not reflect to Gmail by any mean since its a read-only storage and only allow one-way sync (from Gmail to your desktop / web clients). I believe, you shouldn't move or make changes to your Gmail files since it is not permitted by Gmail.
As side note, you can copy your attachments into your desktop, organize and re-arrange all of these files as per your requirements into new directories and then upload them into Google Drive or Amazon Cloud Drive using odrive for later use?