Q1 is, as the title says, is it possible to intercept an object falling into a black hole before it reaches the event horizon?
A large black hole doesn't have crazy tidal forces near the event horizon, and a highly elliptical orbit can bring you arbitrarily close to the event horizon and then back out again without needing any acceleration.
It seems obvious there has to be SOME point at which catching up with a falling object is still possible - if you were far from the black hole, in free fall, you would obviously be able to move something towards the black hole with one hand and catch it with the other.
Q2. What is the latest time/distance at which it is still possible to intercept and retrieve the object?
I've seen people saying that infalling objects actually cross the event horizon in a finite time as their mass contributes to the size of the event horizon and it 'moves up' to them within a finite amount of time, is this true? If so, is this the point where the object actually crosses the event horizon from an external frame of reference and retrieval is no longer possible?
Q3. If the answer to Q2 is "there isn't one", the event horizon moving up idea is false, and the object really does never cross the event horizon from an external frame of reference?
Does this imply that the only matter actually inside the black hole is the matter from its formation and everything else is in a spherical shell around it?
I know there are solutions which say that from the frame of reference of an object fallling into the black hole it crosses the event horizon and reaches the singularity in a finite amount of time, but how is this compatible with the concept of black holes evaporating due to Hawking radiation?
If the infalling object can still be intercepted forever, how can it have entered the black hole before it evaporates?