Are cosmological Black Holes superluminal FTL phenomena?
No. Nothing moves faster than the local speed of light.
What does it mean, "gravity is so strong that not even light can escape from a BH..."?
It's a phrase for introducing the idea to non-physicists starting from Newtonian gravity, and intuitions about the increase of the escape velocity with mass. It's technically true, but not a very good way of describing it.
A more accurate way to describe a black hole is to say that spacetime is twisted round so that the entire future light cone (i.e. 'the future') points into the hole. Locally, spacetime appears perfectly normal, both outside and inside the event horizon.
We can say that getting back from the future into the past means passing backwards through the future light cone, which means travelling faster than light. Hence, it's true to say that a black hole is a region from which even light cannot escape. But it's more useful to say that time points inwards, and the real barrier is not being able to go backwards in time, rather than not being able to go faster than light. They're the same thing, but the former phrasing give the more fundamental reason. Light can't escape from the future into the past, either.
Coordinate systems that try to keep treating the radial inwards direction as spacelike end up in a confused state inside the hole, with the wrong signature, and a divide-by-zero coordinate singularity at the horizon where they switch over, that sometimes deceived people into thinking there was something unphysical about the horizon and interior. During the early days of general relativity this belief was mainstream, with even Einstein denying the possibility of black holes existing. So I don't think it's an unreasonable misunderstanding. But it's not true. Spacetime inside the hole is normal, the local speed of light measured by freefalling observers is the same, and physical laws like the lightspeed limit all obeyed. General relativity only breaks down when you get to the very centre, where the futures all flow in towards the worldline of the central point.
Any future-directed lightcone in empty space acts as a one-way barrier exactly like a black hole's event horizon - this is just the obvious observation that once you pass into the future, you cannot ever get back. Rindler coordinates for a uniformly accelerating observer represents flat, empty spacetime in just this way. Spacetime is filled with 'event horizons', which we cross over all the time. The region on the other side is perfectly normal. It's called 'the future'. And the laws of physics still apply there.