Does anything exist between singularity and the event horizon of a black hole It is said that anything that falls into the event horizon, quickly reaches the singularity. That would imply - there should be nothing between event horizon, and the singularity. Is that true? If not, what is in that region of black hole?
 A: The black hole horizon is global concept, not a local one. Indeed, the formal definition of black hole requires to wait an infinite time to decide whether there is a black hole or not.
This imply that locally, at least according to classical general relativity$^*$, you don't feel anything strange when you cross the event horizon. 
For supermassive the black hole the gravitational tidal forces are negligible and you could probably live years inside the horizon. 
Inside Kerr horizons you could even stay inside forever, or decide to go through other universe! (at least mathematically!)
In a Schwarzchild black hole you can explicitly calculate the maximum (proper) lifetime of a particle radially falling from $r=2GM$ to $r=0$ and is $T=\pi M$, with $M$ the mass of the black hole.
$*$Recent quantum gravity theories suggest that the horizon could be instead a very extreme region. The fuzzball conjecture in string theory, or the firewall hypothesis are some examples.  
A: In the context of the comment you make, then the answer is clear.
There is no stationary "shell" frame of reference inside a black hole event horizon. Nothing can remain stationary and the decrease in the radial coordinate is as inevitable as the increase of the temporal coordinate for something that is outside the event horizon.
Therefore there is nothing (except things travelling towards the singularity) inside the event horizon of a black hole.
