But during your fall you can't bump the wall even a tiny little bit, or you won't make it out the other end. Has to be frictionless!
As for gravity equilibrium, there is definitely equlibrium at the center, with a perception of microgravity due to the pull being outward in all directions. But is that the point of maximum pressure, i.e. the most weight being pressed down from the column of air? I'm not sure it can be, if gravity is actually pulling away from you at that point. So are you weightless but still under intense pressure, or is there a higher pressure (but not weightless) point somewhere out from the center? Does pressure maximize somewhere and then actually decrease as you continue downward?
And has anyone determined where we're going to put 8000 miles' worth of material from our coring project? It's gonna take about 65 to 70 million dump truck loads to haul it off.