Unable to make Sub-folders for "Logins" category.

Creating a new "Folder" ends up under "FOLDERS" and I can't drag it into the "Logins" Category

Well, I would say it makes sense that folders end up in the Folders section of the sidebar, and not the Category section of the sidebar, don't you agree? ;)

As I explained, folders and categories are simply to different ways of organizing your items.

Let's compare 1Password's items with physical objects. You have a shoe, a book, and a lamp. There are various way of keeping track of them. One way is to simply look at what they are. Every item belongs to a category. The shoe is a shoe, the book is a book and the lamp is a lamp. In this sense, all of your books are grouped together even if they are in different physical places. Simply because you think of them in this way.

You cannot change this fact. What you can do is to physically move them around. I might want to put the book on a shelf. I can call that shelf "The book shelf". I don't use the shoe anymore, so maybe I put it somewere in my house where I keep all the stuff I don't need anymore. Maybe that same place contains objects of a different category, like an old lamp.

You should think about the act of moving 1Password items into folders as this act of moving physical objects. Then you see why it makes no sense to move folders to categories. This also means that every 1Password item belongs to one category, and only one.

In my example, "My books" is a category. It contains all of my books. "The book shelf" is a folder. It mostly contain books, but there might be a framed photo there as well. And not all of my books are on that shelf.

As to labeling items as favorites: well, just think of it as a way of labeling things. Like putting a sticker on it saying "This is my favorite thing".

The difference between software and physical objects is that software have the ability so show items that belong to a certain category in a central place. In this case, there is a link in the sidebar for each category. Selecting the category "Login" displays displays all items that belongs to the Logins category. Compare this with a physical object: you have to manually search your house to find all objects that are "books".