Thanks to Steven's help I finally found the solution: it was an item of Safari's menu which was inactive:
Safari: "Developer > Deactivate local file restrictions" was NOT ticked. After ticking this item everything was all right: Juicebox shows immediately displayed without any problems.
Steven directed me to looking into Safari because he had had no problems with my files I had sent to him, neither with Safari nor with Firefox. Even after repeatedly clearing browser chaches and resetting the browser, there was no sign of success. After rebooting my iMac, suddenly Firefox displayed all of the shows! So the reason had to be with Safari itself. And some time later I became aware of this menu option which was not ticked but must be. I don't have a clue why this option was deactivated.
The difficulties with Rapidweaver 6 are smaller because they provide a dedicated HTML stack - this behaves better than the basis stack with text marked as code within this stack. Nevertheless, there are some oddities with editing code in Rapidweaver 6: while typing, the double quotes automatically become a double lower quote etc. I suppose this may be caused by the German localization of the operating system (Mavericks). In case of any problems I'd advise to manually edit the embedded code once Rapidweaver generated its files.
So this story finally came to a good end.