In your showcase there is a menu with different categories. Is there a way to put files in different folders according to this? I assume this can be handled by the HTML 5 upload extension?

Yes, you can do this. You can use dynamic paths with HTML5 File Upload. Please check the following tutorial, that explains this - www.dmxzone.com/go/32181/sending-additional-data-with-the-uploaded-files

Thanks for the hint!