Things without mass, instead, can only travel at the speed of light (photons for instance).
Finally, there is a quirk in the math that would allow for the appearance of faster than light travel. If you compress the spacetime in front of you and expand it behind you you could can move faster than light without turning into a black hole or needing infinite energy (Google Alcubierre drive for more information). It is only an appearance than faster than light travel because you would still move at sub-luminal speed in your bubble of "normal" space time, but the compression/expansion effect would drag you through space-time at faster than light speed. This, however, require so called "exotic matter", ie matter with negative energy density (this is not anti-matter, but matter that has a repulsive gravitational field) and it is probably only a quirk of the math and nothing more.
You are quite right that no matter nor energy nor information is traveling faster than light here.
That way, there really isnt a point that is traveling or moving, its just our perception mistaking it for a point because it looks and move like one.
The thing is that lots of our 'concrete' real world objects have more in common with the later pointer point than with physical reality. Concreteness is a bit of an illusion, it's all wave functions at the bottom.
(Of course, real world objects still can't go faster than light.)