After a matter enters the event horizon of a black hall, is it possible for it to orbit the point of singularity without merging with it?
Obviously, it is not something we can observe, so my question is about the speed the matter needs to move behind the event horizon to make this happen. Can this speed be slower than the speed of light?
For a standard Schwarzschild black hole, once you pass the event horizon, the radial coordinate becomes time-like. That is, all paths lead to the singularity no matter what your velocity. Therefore, no such orbits are possible.
For charged black holes there are two horizons. An outer event horizon and inner Cauchy horizon. In such a case, one side of the Cauchy horizon has closed space-like paths and the other side contains closed time-like paths.
In this case it's possible to find a path that can pass these two horizons and return to the original point.
No, it is not. A technical answer is involved. This is the simple answer.
All trajectories are required to move forward within the confines of their future light cone. The light cone is defined by the trajectories that light can take forward from an event (so called forward pointing null world-lines). Inside the event horizon, all future light rays point towards a smaller radial coordinate. That means as you move into your future, you must move closer to the singularity. It becomes not a place, but a time in your future, and simply cannot avoid it.
Meanwhile, all of your past exists at larger radii. Every light ray you see comes from larger radii, no matter which direction you look. In terms of the Schwarzschild metric, this is a result of $g_{tt}$ and $g_{rr}$ swapping signs inside the horizon.
Regarding the proper time you experience: much like the twin paradox, the inertial path (free-fall) has the longest proper time between two event. Any acceleration along the way reduces you integrated proper time. Thus, using super-rocket to get into an (unobtainable) orbit, or trying to slow you fall, results in less proper time between now an oblivion.
tl;dr summary: Inside the event horizon, the future propagates to smaller radii, not larger time, and the singularity is an unavoidable time in your near future.
