Inside the event horizon of a black hole, our understanding of spacetime breaks down according to our current theories of physics. The equations of general relativity, which describe the curvature of spacetime in the presence of mass and energy, become singular at the center of a black hole, known as the singularity. As a result, it is challenging to make precise statements about the nature of spacetime within the event horizon.
Regarding the distance between points inside a black hole, it is not accurate to say that there is an infinite distance between any two points. While our conventional understanding of distance and geometry may not apply in the same way within a black hole, it doesn't necessarily imply that the distance is infinite. The breakdown of spacetime near the singularity suggests that our current understanding of the laws of physics may not be sufficient to describe the nature of spacetime under those extreme conditions.
It's worth noting that the gravitational force inside a black hole, including the event horizon, is still present. Gravity arises due to the curvature of spacetime caused by the mass of the black hole. As long as an object or particle is within the event horizon, it will experience the gravitational pull of the black hole and be drawn toward the singularity.
As for the presence of another black hole within the event horizon, it is not well-understood what occurs at the singularity. The singularity is often considered a point of infinite density, where our current laws of physics break down. Therefore, it is unclear what exactly happens to matter and energy as they approach the singularity. Some theories suggest the possibility of the formation of a new spacetime region or the emergence of a new universe, but these are highly speculative and still under active research.