  We present here the characterization of the night sky-brightness at the
near-infrared, the telescope seeing, and the fraction of useful time at the
Calar Alto observatory. For this study we have collected a large dataset
comprising 7311 near-infrared images taken regularly along the last four years
for the ALHAMBRA survey (J, H and Ks-bands), together with a more reduced
dataset of additional near-infrared images taken for the current study. In
addition we collected the information derived by the meteorological station at
the observatory during the last 10 years, together with the results from the
cloud sensor for the last ~2 years. We analyze the dependency of the
near-infrared night sky-brightness with the airmass and the seasons, studying
its origins and proposing a zenithal correction. A strong correlation is found
between the night sky-brightness in the Ks-band and the air temperature, with a
gradient of ~ -0.08 mag per 1 C degree. The typical (darkest) night
sky-brightness in the J, H and Ks-band are 15.95 mag (16.95 mag), 13.99 mag
(14.98 mag) and 12.39 mag (13.55 mag), respectively. These values show that
Calar Alto is as dark in the near-infrared as most of the other astronomical
astronomical sites in the world that we could compare with. Only Mauna Kea is
clearly darker in the Ks-band. The typical telescope seeing at the 3.5m is
~1.0" when converted to the V-band, being only slightly larger than the
atmospheric seeing measured at the same time by the seeing monitor, ~0.9".
Finally we estimate the fraction of useful time based on the relative humidity,
gust wind speed and presence of clouds. This fraction, ~72%, is very similar to
the one derived in Paper I, based on the fraction of time when the extinction
monitor is working.
