can I have some photos in one album but in no other album?

You can add and remove photos freely in any album you create yourself, but you cannot change the albums that are automatically created for you by Photos. The automatically created albums are based on all photos in your library, according to the rules specific for each album. And you will see many photos in in several albums.

But with the albums you create yourself, you are free to aadd and to remove photos.

A smart album with the rule "Album is not any" can help to find photos that are not yet in any of your albums. But you cannot check in how many albums a photo is.