Robert, regarding a possible WW I origin for the saber, IMO that it is not possible because it�s the wrong type of sword. Sight unseen, my guess is that it is 1935 (�G�) dated, as the visible German Army property markings seem to indicate.
As Chris very correctly commented on there are a lot of fake �SS� items in circulation. In my experience it greatly exceeds by a very large margin the amount of genuine period items. In the mid to late 1960�s (?) fakers were creating fantasy etched blade �SS� bayonets from originals which were sold at relatively low prices. Documented fake items themselves of various types were made as early as the 1950�s.
Back then the financial gain was not that great - but so was the cost of the items themselves. With good condition bayonets, daggers and swords (etc.) sometimes selling for as low as $15.00, $20.00, $30.00, or $40.00 (and poor condition items perhaps at half that amount). So there was experimentation (especially the lower cost items), but high end items were also targets for counterfeiters. With what was learned in the counterfeiting process sometimes making its way to higher priced items. Some counterfeiting operations produced a lot of fakes. Some just one or two. Sometimes made from originals, but others like the so-called �Krupp� daggers completely new creations.
Some examples of fake �SS� items that are currently in circulation: A fake �SS� dress bayonet made from an original (which had other additions as well) modified to try and help it sell at a much higher price than a �plain jane�� dress bayonet would have sold for.