Q: Are photos duplicated when I move to a new album in icloud?

No, albums are just referencing the photos in the library.  You can add a photo to as many albums as you like without duplicating it.

And you cannot move a photo from a moment.  Every photo will always be in exactly one moment, only deleting a photo from the library will remove it from its moment. when you add aphoto to an album it will stay in the moment an in all other albums it is already in.