  In Paper I, we followed the evolution of binary stars as they orbited near
the supermassive black hole (SMBH) at the Galactic center, noting the cases in
which the two stars would come close enough together to collide. In this paper
we replace the point-mass stars by fluid realizations, and use a
smoothed-particle hydrodynamics (SPH) code to follow the close interactions. We
model the binary components as main-sequence stars with initial masses of 1, 3
and 6 Solar masses, and with chemical composition profiles taken from stellar
evolution codes. Outcomes of the close interactions include mergers, collisions
that leave both stars intact, and ejection of one star at high velocity
accompanied by capture of the other star into a tight orbit around the SMBH.
For the first time, we follow the evolution of the collision products for many
($\gtrsim 100$) orbits around the SMBH. Stars that are initially too small to
be tidally disrupted by the SMBH can be puffed up by close encounters or
collisions, with the result that tidal stripping occurs in subsequent periapse
passages. In these cases, mass loss occurs episodically, sometimes for hundreds
of orbits before the star is completely disrupted. Repeated tidal flares, of
either increasing or decreasing intensity, are a predicted consequence. In
collisions involving a low-mass and a high-mass star, the merger product
acquires a high core hydrogen abundance from the smaller star, effectively
resetting the nuclear evolution "clock" to a younger age. Elements like Li, Be
and B that can exist only in the outermost envelope of a star are severely
depleted due to envelope ejection during collisions and due to tidal forces
from the SMBH. In the absence of collisions, tidal spin-up of stars is only
important in a narrow range of periapse distances, $r_t/2\lesssim r_per
\lesssim r_t$ with $r_t$ the tidal disruption radius.
