How to organize photos in albums and remove them from main view on iCloud?

The "Library" (what I think you mean by "main view" and "main photos") contains all of your photos, whether or not they are also shown in one or more albums. If you delete a photo from the Library it is deleted everywhere including any albums where it is displayed.

Note that this does not take up more iCloud storage; there is only one photo stored and it is displayed in multiple places.

You can add photos to albums in the iCloud Photos app by dragging them from the Library to an Album in the sidebar.