That's not an exhaustive definition; for example, German battlecruisers have lighter armament, but the same protection as battleships. And Russian "Izmail"-class battlecruisers were supposed to have even better protection than many cotemporary battleships.
Again, no. You are trying to use a functional classification, while it actually was technical.
To put it simply, battlecruiser is a "not balanced" capital ship. It sacrificed some of standard capital ship qualities - like armor, armament, seakeeping ability, ect. - for a speed advantage. Generally it was a forced solution; 1910s - 1920s powerplants were simply too big and heavy, so to get a 5+ knot speed advantage your powerplant needed to be enormous. You could not build balanced capital ship that would also be fast - you needed to sacrifice some other quality.
Fast battleship is a balanced fast capital ship. The advances in powerplant designs by 1930s essentially allowed to double output in a half of old powerplant size/mass. So it became possible to just build high-speed capital ships, without the need to sacrifice anything.
Kevlar plates over vitals, as far as I knew.
