quantum field theory - Why is there a flux of radiation in the Hawking effect but not in the Unruh effect? (and other questions)

This question is slightly related to this one Do all massive bodies emit Hawking radiation?, which I think was poorly posed and so didn't get very useful answers. There are several questions in this post so I hope people who answer will follow the question marks and give their opinion on each one.

Let's look at flat spacetime first. Inertial observers detect no particles in empty space. Non-inertial observers do detect particles because there is a non-trivial Bogolyubov transformation that mixes positive and negative frequency modes of the matter field. And finally, if the non-inertial observers see a horizon as in the Unruh case, the spectrum of detected particles is precisely thermal.

Now look at a black hole spacetime. Free falling observers will not detect any particles but distant/stationary observers will detect a flux of radiation from the black hole outward to infinity. Q1: Why is there a flux in this case and none in the Unruh case? Shouldn't the two situations be nearly identical for the case of a very large black hole or very near to the horizon? How would you physically distinguish between the two anyway? (Maybe this is equivalent to asking why the black hole should lose mass and evaporate)

Q2: Is it natural to expect that an observer who is not in free fall but is not stationary either (and is on some weird trajectory) will detect particles but that they will not be in a thermal state?

For massive compact objects without a horizon, free fallers should see no particles but other non-inertial observers should detect particles because of the Bogolyubov transformation as in the Unruh case. This probably depends a lot on the answer to Q1 but Q3: suppose you bring such an object arbitrarily close to the point of forming a black hole with a horizon (by adding mass) -- what would a stationary observer see? Would radiation and evaporation be observed only once the horizon is formed?

Q4: In the Unruh case, the energy from the radiation is accounted for by the agency that accelerates the detector. In the black hole case, it is accounted for by the evaporation of the black hole. How is it accounted for in the case of a stationary detector outside a massive compact object without a horizon (which doesn't evaporate)?