Earlier quoted context omitted.
What exactly is the "density" of a black hole? As I understand, a BH is a singularity, so all mass is at one point which means all BHs have the same (infinite) density. Is it a kind of "virtual density", e.g. the mass of the singularity devided by the schwarzschild radius or the event horizon?
Density is mass divided by volume. Volume of BH is defined by event horizon. Singularity is a result of applying a theory of relativity in a case where we know relativity doesn't work, so it's unlikely it's real.
The event horizon is a three-dimensional null hypersurface, though, encompassing a four-dimensional spacetime "volume". You are probably referring to the two-dimensional apparent horizon, which depends on the spatial slicing.