You must try Copywhiz - http://www.conceptworld.com/Copywhiz
It does exactly this. Scheduling too in the latest version. And next week it will be on BitsDuJour at 40% off.
I have developed this software.
Copywhiz helps you quickly copy pre-defined set of files, right from the Windows File Explorer context menu. You can pre-define the source files and save it as project. Then just run the project from the Copywhiz menu - http://www.conceptworld.com/Copywhiz
You probably don't need a file manager. But a file copy software that will help you delete/move in a massive way. You can try Copywhiz - http://www.conceptworld.com/Copywhiz
You can use Copywhiz to copy all media files to a folder. Copywhiz can copy files based on file extension. So you can just copy all jpg, png, mp4, mp3, mpeg etc in to separate location. Copywhiz also has an option to copy all files into a single folder so that you don't have to dig into each folder. If a file with same name exists, then it can rename automatically - http://www.conceptworld.com/Copywhiz
Copywhiz can do that (almost). You would configure Copywhiz to copy a file (sample dummy file) to a new destination folder each time. This new destination folder is based on current date. Also it has the option to schedule (Every week). So you will see a folder created automatically with that folder name.
More about Copywhiz - http://www.conceptworld.com/Copywhiz
Copywhiz can do it easily for you. You can extract certain types of files (video, images) from several folders and move them somewhere else. This way you can organize your videos and images (based on name, type etc) - http://www.conceptworld.com/Copywhiz