Your intuition is incorrect; time does not reverse inside a black hole. Time passes in a fully "regular" manner for an observer within a black hole, just as it does at the horizon. As you indicated, the halting of time at the horizon is a phenomena that only an outside observer can witness.
You will never see the clock hit the event horizon if you are sitting outside the event horizon watching it fall in. The clock will slow as it reaches the horizon, and it will run slower and slower. However, time does not cease at the event horizon in any sense. It is just that there is no escape from it.
The event horizon is a theoretical boundary in space-time geometry that marks the point at which objects can no longer escape the gravity of a massive body. An object passing this point would be destroyed by this force. Although light cannot escape from inside a black hole, anything falling into it could remain alive indefinitely by entering a new state of being: eternal unconsciousness.
Black holes are very dense objects made up of many electrons orbiting around a nucleus. They have a mass greater than the value given by Einstein's formula for the amount of matter that can exist inside a spherical shell with a radius equal to the distance between two galaxies. This shows that black holes may contain more than just empty space; they may also contain particles such as electrons.
In general relativity, the event horizon is the boundary of an invisible region called the "shadow" of the black hole. All objects with less mass than the black hole's mass will fall inside the event horizon when they cross its orbit.
When you reach the singularity of a black hole, time stops for you since you have been obliterated. Time does not halt for you just because you pass through the event horizon of a black hole. Instead, you will experience infinite gravitational time dilation as you are stretched out over an infinitely large area while remaining motionless.
This means that you will never age and die in a black hole, but instead you will be crushed into nothing by the force of gravity over an eternity of time.
The reason we know time stops in a singularity is because no signal can escape from it. If time stopped for everyone, then there would be no way to tell if a star went supernova or not, or if a galaxy collapsed into a black hole or not. Since we can't make such observations, time must stop for those inside the singularity.
In fact, according to general relativity, nothing can escape the pull of a black hole except information. That's why many scientists believe that black holes may actually be portals to other dimensions where information is transmitted between worlds.
However, this isn't the only reason time might stop inside a black hole. There could be any number of reasons why this might happen, including but not limited to: quantum mechanics, string theory, etc.
Because the forward light-cone in a black hole is directed towards the center and the backward light-cone is directed outward, it is impossible to describe time-reversal in the conventional sense. Hawking radiation is the only method for anything to escape from a black hole. So, if something falls into a black hole, it will be lost forever.
However, according to Einstein's theory, the object's mass and gravity persist in the form of a severe deformation of space and time around it. The black hole is a distortion of space and time. The passage of time slows as you move closer to a black hole compared to the flow of time far away from the hole. This has important consequences for those who fall into a black hole.
Black holes are not actually dark or empty, but they do play host to some very strange things. Space and time near a black hole are distorted in a way that no physical object can escape its influence. A particle orbiting a black hole would follow an elliptical path, with one end approaching close to the black hole while the other was far away. After several orbits, the distant end would reach far beyond what could be measured by any instrument and would appear to go on forever. There is no known mechanism by which particles could remain in orbit around a black hole, so if there were any in our galaxy, they must have entered through the event horizon.
Black holes were first theorized by German mathematician Karl Schwarzchild in 1916. Since then, many scientists have studied their properties because they are interested in understanding more about the nature of gravity.
In addition to being interesting in themselves, black holes are relevant to ideas about how the universe began since they are one possible outcome of the collapse of a massive star.