Is there a way to move photos to specific albums and remove from the ‘all photos’ section?

You can't do what you want.

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.

Photos for Mac has a smart album feature that will find all the image sin your Library that are not in album, but that's not on iOS. Feature requests go here:

Feedback - Photos - Apple

UCAyy wrote: After moving selected photos to an album, can I hide those photos from the “All photos” library and still view them in the album?

This question is not really connected to this thread, and putting a new question in a previous thread is called "hijacking." But that's just for future reference-- to your question:

Those places called Library and Recents, etc, are not real albums--not like the ones you make yourself. These are special pre-set ways to view your pictures. The "LIbrary" view shows all the pictures in your Library in the order your pictures were taken. The "Recents" view shows all the pictures in your Library in the order they were added to the Library-- not necessarily in the order they were taken. This can't be changed. These albums always provide the same view so that, when something goes wrong or seems off, you (and we) can depend on them always showing the same thing, and there's no chance that someone snuck in and changed the order or removed pictures.

So if you delete a picture from the Library or from Recents, it must be deleted from the phone. (Of course, it really goes into the Recently Deleted view, and you have 30 days to change our mind.)

Hiding pictures is a system-wide choice. You can imagine the consternation if you were to hide a picture from several albums, and then realize someone was looking at that picture in an album you had forgotten about!

I would be sure to file a feature request. That feature has been available on Macs since day one of Photos and they show no sign of adding it to iOS. The squeaky wheel gets the oil and all that.

After moving selected photos to an album, can I hide those photos from the “All photos” library and still view them in the album?