  We study in detail the dynamics and stability of marginally trapped surfaces
during a binary black hole merger. This is the second in a two-part study. The
first part studied the basic geometric aspects of the world tubes traced out by
the marginal surfaces and the status of the area increase law. Here we continue
and study the dynamics of the horizons during the merger, again for the head-on
collision of two non-spinning black holes. In particular we follow the spectrum
of the stability operator during the course of the merger for all the horizons
present in the problem and implement systematic spectrum statistics for its
analysis. We also study more physical aspects of the merger, namely the fluxes
of energy which cross the horizon and cause the area to change. We construct a
natural coordinate system on the horizon and decompose the various fields
appearing in the flux, primarily the shear of the outgoing null normal, in spin
weighted spherical harmonics. For each of the modes we extract the decay rates
as the final black hole approaches equilibrium. The late part of the decay is
consistent with the expected quasi-normal mode frequencies, while the early
part displays a much steeper fall-off. Similarly, we calculate the decay of the
horizon multipole moments, again finding two different regimes. Finally,
seeking an explanation for this behavior, motivated by the membrane paradigm
interpretation, we attempt to identify the different dynamical timescales of
the area increase. This leads to the definition of a ``slowness parameter'' for
predicting the onset of transition from a faster to a slower decay.
