Famous Funnies isn't Golden Age, is it?

Famous Funnies started in 1935

To my understanding, Action Comics #1 is the beginning of the Golden Age and from about 1833 or 1897 to (pre) June 1938 is the Platinum Age.

So does the Golden Age count as the beginning of the Superhero genre, or as the beginning of comics no longer being only reprints of older comics ?

No. Famous Funnies is the beginning of the Golden Age and of comic books. Action 1 is the beginning of Superheroes as a main feature of comics.