How can I move a video from Photos to a separate folder on my iPad?

I'm not sure what you mean by "Photos File," but to add a picture or video to an album you select the picture and tap the 3 dots, More (…) and choose Add to Album. It will then show a list of your albums. To create a new album, you can go to the Albums section and choose Create. See this:

Create photo albums on iPhone - Apple Support

You said "move a video out of my Photos file" and I worry that you mean you want to remove a picture from the Library view. Of course, if it's not in the Photos Library, then it can't be anywhere. You can imagine a system where a picture is either in a "Photos file" or it's in an album, but that would be a system in which pictures can only be in one album, like the picture is a little print that has to be here or there, but not both.

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. 

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.

If a picture disappears from the Library, then you couldn't have it to "put into" another album.

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. 

I hope this helps…