MediaLibrary folders are file system folders. So you can use CMS.IO.Path which includes System.IO.Path to check if it exists. Which file system path is used is configured in the media library settings and the default path is ~/sitename/media/.
The MediaFileInfo object contains only additional data for the file in the file system, like file title or description.
If you want to move it, I would delete the old one and create a new one in the new location.
If you want to keep some properties you can map it before doing this, e.g. "newFile.FileTitle = oldFile.FileTitle".