Remove from album is missing

Where are you looking for the Remove command? It should be near the bottom of the Image menu when one or more item(s) is/are selected and at the bottom of the context (right-click) menu in normal user-defined albums. You can't remove items from Smart Albums or most system-defined albums.

If you're talking about removing a picture from Recents or Library or any of the views that Apple provides, then those aren't exactly Albums, like albums you make. These are special views of your pictures. Recents shows all your pictures in the order they were added to the Library, and Library shows all the pictures in the order their metadata says they were created. These always provide the same view so that, when something goes wrong or seems off, you (and we) can depend on them showing the same thing, and there's no chance that someone changed the order or removed pictures. Removing a picture from these views would mean that the picture no longer exists in you Library (except, maybe, in Recently Deleted.)

So when you click on a picture and choose trash, an Album will offer you the option of removing the picture from the album or deleting it from the Library. But when you choose trash from a pre-set View, then you're only option is to delete the picture from the entire Library of pictures.

There are no duplicates. It's the same file showing in different places.

Photos, (like iPhoto, Aperture, Music, iTunes) is a database. This means it can be very flexible and powerful, if sometimes a little confusing. The library is the core of the app. Every image is in the library. Albums are virtual, and are just subsets of the library. In fact, Albums are not places, they are lists - instructions to the app to 'display this group of images together'. So images do not get "moved" to Albums, they get added to that particular list. This means that an image can be in more than one album but use no extra disk space. Similarly in the Music app, all the tracks are in the Library and can be added to any number of playlists.

In a Mac:

If you're trying to organise your Library and want to find images not in albums, then a simple Smart Album

File -> New Smart Album

Album -> Is Not -> Any

will find these images. As you add them to albums they will disappear from the Smart Album.

On iPad or iPhone, which do not currently support Smart Albums:

Check out HashPhotos

https://apps.apple.com/ie/app/hashphotos/id685784609

It integrates with Photos on your iOS device and adds a Smart Album feature. Using this app a search

!#inalbum

Will find images not in an album

(Hat tip to User ukSamo for the recommending this app.)