Photos
Is it possible to move pictures out of the PHOTOS Library into specific albums in a manner that the pictures will no longer show in the Library feed?
MacBook Air
No. The Library includes all photos, whether or not they are in one or more albums. Note that they do not take up storage space. There is only one photo stored and it is displayed in multiple places.
If you want to identify photos that are not included in any Album, you can create a Smart Album with the condition: Album -- is not -- Any using the Photos File menu New Smart Album.