Would energy be seen to "flow" to the outside of the black hole? Through what mechanism?
The observer inside the event horizon does not observe Hawking radiation--- this is a pure external effect.
This is an incomplete answer, but I would bring two important points here:
1) When observer moves freely in GR, he/she observes locally flat spacetime up to quadratic corrections in 3-distance from his/her worldline. Hence, if you are falling into a black hole, you shall see the same as what you would see, if you were in Minkowski spacetime throughout all your infall, unless you start measuring the tidal forces. Hence, you shall see no Hawking radiation generated around you at all, until you come so close to the singularity, that the tidal forces shall become very strong and you shall eventually observe local generation of particle-antiparticle pairs around.
However, this doesn't exclude the possibility of observing some flux falling with you from the infinity into the black hole.
2) The notion of particles in GR depends on your reference frame. If you imagine an observer located above the event horizon, accelerated in such a way that he/she has stationary spatial coordinates, he/she will not be moving freely due to acceleration and shall see particles/antiparticles generated around, some of them falling under the horizon, and some of them flying away from the black hole. If you consider some static asymptotically flat coordinate system, you shall see that some particles in this system shall escape to infinity and shall be visible to the remote observers, moving freely with respect to that system.
To conclude, you shall not observe Hawking radiation generated around you, though you might possibly see already existing particle-antiparticle background (possibly, exactly Hawking radiation).
An observer inside a black hole is impossible because a black hole has no internal structure (otherwise it would be possible to transfer information from inside by moving massive bodies.
Also no information can be under the horizon because this would mean information loss which is impossible thermodynamically.
So any black hole is an uniform body without internal structure.