This is a core benefit of using a CMS, and can be done quite easily with Content Manager. Go to Administration, Content Manager. Find the feature you want to move in the list, and click the Publish/Delete link. You can then add it to the new page, and delete it from the old using the buttons in the Published column.

Jamie

You can have multiple instances of Shared Files, either together on one page or on separate pages. Then just upload one subdirectory's files into each instance. But as Asad said, each individual instance of Shared Files will only "know" about the files you upload into it, not what's in the others.

Jamie