Remove pictures from library and put them into a separate folder.

Nope. Photos app does not provide this. Not short of exporting a copy, or exporting and deleting the copy in Photos or iCloud Photos.

If you want to completely manually manage some or all of your photos, sure, export them some or all, and don’t use Photos app or related interfaces and tools again.

Any photo storage app that tries to provide this file-based feature will be chasing corruption problems and re-scanning directories forever too, as users inevitably move or delete or rename the files, or as whatever file hosting service being used glitches. Then there’s the “fun” of managing duplicate photos, because there will always be duplicates. And does that app then take over any photos found in file storage?

(Yes, technically, it’s possible for an app developer to create an app that uses what amounts to a file system (FUSE) to do what you want and also maintain the photo library, but that’s a whole lot of work for what is likely a small market. The IBM Rational ClearCase app does this with what they call VOBs, and there are source code control systems that can do things similar to this file system presentation. I’ll leave it to you to convince a developer to create this app.)

The Apple solution is to keep photos in the Photos library, and use albums to organize the photos. Albums provide sets of photos, and photos can exist in no albums, one album, or many albums, however the user decides ro organize them. But Apple doesn’t provide a supported means to access photos in the library using file commands and tools, and doesn’t allow an iPhone user to move the original somewhere other than its place within the photo library. Exports or copies yes, or export-and-delete yes. But Apple Photos wants to keep the original, short of explicit deletion.

The Library is all of your pictures. If you remove a book from the New York Public Library, it's not there, anymore. It's gone. That's what the Library is in Photos. What you're suggesting makes no more sense than wanting to remove a book from the Library but keep it in Fiction.

This provides incredible versatility. In Photos, pictures aren't exactly "in" an album. When you "put a picture into an album," its name is added to a list of pictures from the Library that display together when the album is clicked, kind of like a music playlist, but for pictures. So two albums can both have the same picture name in their lists (like two playlists with the same song,)  and that picture will show up when you click either album, but there's only one picture file-- it's just on multiple lists. And when you remove a picture from an album, its name remains in the lists of other albums, and the file still remains in your Library. You don't get fewer pictures in your Library because you remove one from an album; you just get fewer names in the album list.

Continuing the metaphor above, Photos' albums are kind of like the old card catalogs at Libraries-- the book can be listed in several cart categories, but there's only one book.

So albums give a specific view of your pictures. The picture of "Aunt Ethel at the Grand Canyon" can be in the "Aunt Ethel" album with other pictures of Aunt Ethel, and it can also be in the "Grand Canyon"  album with pictures of other people at the Grand Canyon. And it can also be in a the "September 2015" album with other things that happened then. Each album is pointing to a single file stored in the Photos Library, so having pictures in multiple albums takes up no more storage space. As you can imagine, this is very powerful in organizing pictures.

There are special views provided by Apple. The Library View is provided by Apple to give a view of all of the pictures in the entire Library in the order of their "taken" dates or their "added" dates depending on a your menu choice. You can't remove a picture from the Library View, because that would be deleting it entirely. The Hidden View shows all the pictures from the entire Library that you have marked to be hidden. You can't change how these views work. 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.