It's not an illusion at all, and neither observers reference frame is more privileged than the other.
There is no global reference frame that allows you to say that the objects actually fell in and hit the singularity inside the hole long before you see the final image
I am not talking about any particular observers. I am talking about invariant properties of the spacetime geometry and invariant curves within that geometry. Nothing I have said depends on any particular choice of observers. I only phrased it in terms of what a particular observer sees because the post I was responding to was asking about what can be seen from outside the horizon. I could just as easily have phrased it in terms of what null curves intersect with a particular timelike curve; the underlying geometric facts, and the fact that they are invariant, are the same either way.
> There is no global reference frame that allows you to say that the objects actually fell in and hit the singularity inside the hole long before you see the final image
Yes, there is. There are a number of frames that cover both the exterior and interior regions; for example, Painleve coordinates, Eddington-Finkelstein coordinates, and Kruskal coordinates.
I'm not sure what "extra" means, but a general rule of thumb is that the time to fall goes like the 3/2 power of the radial coordinate you are falling from. (Strictly speaking, this is the time to fall to the singularity, not the horizon, but for falling in from large radial coordinates, which will be the case for virtually all cases of interest, the difference is small.) The only technical complication is that this rule is true if the time and radial coordinate are in units of the Schwarzschild radius of the hole; you then have to convert to conventional units. A couple of specific examples:
Black hole of one solar mass, observer falling into the hole from a distance of 3 million kilometers (which is about 4.3 times the radius of the actual Sun--the distance is chosen for reasons that will appear in a moment). This makes the radial coordinate 1 million, 10^6, in units of the Schwarzschild radius of the hole (which is 3 km), so the time to fall will be 10^9, 1 billion, times the light-travel time across that distance, which is 10 microseconds (10^-5 seconds). So the time to fall will be 10^4 seconds, or about 3 hours.
Black hole of one million solar masses, observer falling into the hole from a distance of 30 billion kilometers (or about 5 times the semi-major axis of the orbit of Pluto around the Sun). Here the radial coordinate is only 10^4 in units of the Schwarzschild radius, so the time to fall will be 10^6 times the light travel time across that radius, which is 10 seconds (a million times 10 microseconds). So the time to fall will be about 10^7 seconds, or about 4 months.
Yes, but things can still fall in and hit the singularity inside during that time. You can't see the inside from outside, but you can still calculate that it is there based on observations you can make outside.
> if you are a conscious very resilient little particle doomed to fall into a black hole... do you really appear from the outside to be falling in until the black hole evaporates?
Sort of. If you are watching from outside, when the hole finally evaporates, you will see a big flash of light that includes images of everything that fell into the hole before it evaporated away, at the instant those things crossed the hole's horizon. Up until that point, yes, you will see infalling objects appear to gradually slow down as they approach the horizon. But that is only a sort of optical illusion; the objects actually fell in and hit the singularity inside the hole long before you see the final image of them crossing the horizon.
> is a black hole sort of a time machine to the end of the universe where in the short process of falling in you get to watch the whole history of existence pass you by
No, it's not. If you fall into a black hole, you will only see a short portion of the future of the rest of the universe from the time you started falling. The rest of the future of the universe will never become visible to you.
> is there some third option
No.