The Appalachians WERE levelled. When they were formed they were like the Himalayas. The "weathering" event referred to is presumably the erosion over millions of years that finally left the "nubs" we have today.
These "nubs" are actually the pattern left by the differential erosion in the folds at the roots of the mountains. That is, the peaks we see are not eroded versions of the former peaks.
Correct. The Massanutten Mountain, for instance is the bottom of a downfold (syncline). The 'up' portions of that fold are long gone.