Re #10. Well, I guess Berlin doesn't have an U-Bahn system according to this over-simplified definition -- even though there are no grade crossings on the U-Bahn system that I know of. Yes, much of Berlin's U-Bahn is above ground and much of the S-Bahn is underground. Still, they are obviously quite different systems built according to widely differing standards. When it comes to the streetcar/tram/Straßenbahn system in Berlin, in some places it runs in its own lane, in others it is mixed in with traffic. What amazes me is when I see the public transport in other German cities, and their supposed U-Bahn is what would be called a Straßenbahn in Berlin -- even if it does run underground for part of its journey, as the streetcars in San Francisco do.
(On the US side of things, the Chicago subway system is called the "El" because it historically ran on elevated tracks within the city before parts of it were moved underground. Even today, there are a few areas outside of the city proper on minor lines where the El has grade crossings. Still, no one would confuse the El with a streetcar/tram, and it is more like a regular train system than the light rail systems in the US that I have seen – although I suspect that it could be considered as such by some understandings of the phrase -- the El is far older than the phrase "light rail".)
Summary: You can't get dogmatic about what exactly the various terms mean in either German or English. Transportation concepts are interpreted in various ways according to local needs and the history of their local development.