Good point. In a world of 30-fps-locked games, a game that is engineered to run with your framerate just feels right, even if you're "only" playing at 60Hz.
No, the game uses frame delta times rather than a set tick rate per second.
(In general it's how most games already work; it's just that it's normally convenient to set it at a fixed rate to make some things like physics more deterministic, and it gives a nice target performance/budget).
Not if the cinematics are synced to a global timer instead of the frame rate. Then when the frame rate is too low the game skips some frames to keep up.