How to save photos then delete from All Photos

A Lightroom folder is not like a folder on your computer. It is more like a group to organize your albums. You can remove a photo from an Album without deleting it. You can also delete albums from folders without deleting the images in it. If you delete a photo from anywhere, it deletes it from everywhere. 

Everything is stored in All Photos, this is the main Library.

When you add a Photo to an Album, think of it as you are adding/moving an alias of that photo rather the photo itself. Or alternatively you could say you are assigning it to an Album.

You cannot delete out of All Photos without deleting from the Cloud. The Cloud Based Lightroom cannot reference local disc based photos as Lightroom Classic does, everything is stored in the Cloud.

It is my understanding that folders will enable you to group collections together as a method of organizing collections. But I don't think it's possible to move individual images into folders. You can try, but I don't think you will be successful.

A photo only exists physically one time. That photo can be placed in many different albums because those albums are just separate entities within Lightroom. But the actual physical file only exists once. So if you go to All Photos and delete the actual photo file, that will remove that image from any and all albums in which you have placed that photo.