No, speed of light will not move faster inside in the event horizon. It is still at the same speed.
But the spacetime is so distorted that a photon will start orbiting the singularity, thus it doesn’t get out of the event horizon.
But the spacetime is so distorted that a photon will start orbiting the singularity, thus it doesn’t get out of the event horizon.
The link you post describes a region in certain conditions where light can orbit not that that is the fate of all light falling into a black hole.the end talks about the always orbitally unstable regions beneath that being referred to here.