A couple excerpts from the Wiki article on black holes that may (or may not) answer your first question:
1)'...the light is running on a spacetime "treadmill;" the light is moving away from the black hole at the rate of
c, but the spacetime is being sucked into the black hole at the same rate, so the two cancel each other out, much like a treadmill.' Or, I think a better metaphor might be, it's like trying to to run up the down escalator that is moving as fast as you can possibly run.
2)'Within the ergosphere, space-time is dragged around faster than light—general relativity forbids material objects to travel faster than light (so does
special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.'
So I think -- and I'm no physicist, so feel free to suspect I'm talking out my ass, for I surely think so -- that nothing is really pulled faster than light. It is merely that the mass of the thing means its escape velocity prevents light (and mass and information) from moving out beyond its event horizon. Photons don't move into the black hole at superlight speeds, and nothing is pulling them in at superlight speeds.
To answer your second question, earth would continue to move with whatever momentum and direction it had, according to Newton's laws. It isn't drifting away, really. It was in motion and would stay in motion, along that same vector and with the same speed. Next, it would start drifting toward whatever object was massive/close enough to make its own little well or dip in the grid sheet of these animations. Newton said that every object in the universe attracts every other, proportionally to its mass and inversely proportionally to the distance between the two objects. The earth and some other massive object would find each other (this is too cutesy, really, for I make it sound like lovers running slow motion toward one another in some perfume advert) and meet in a lovely marriage (I may as well go for broke with that metaphor) of orbits around their common center of gravity.
But as I say, I'm just a student of these things and may be wrong. Or I might be right but totally unclear in my explanation, and if that is so, wait for a real scientist to come and answer with more clarity and accuracy.
BTW, I like Brian Greene a lot. While reading his book
The Fabric of the Cosmos, I had the only moment I ever felt I got what the hell a Higgs field was--of course, a week later, I no longer really understood it, but for a moment there, it seemed to be within my grasp. What more can I ask of a popular science book explaining very technical matters?