  We present a detailed study of the Planck-selected binary galaxy cluster PLCK
G165.7+67.0 (G165; $z$=0.348). A multiband photometric catalog is generated
that incorporates new imaging from the Large Binocular Telescope/Large
Binocular Camera and Spitzer/IRAC to existing imaging. To cope with the
different image characteristics, robust methods are applied in the extraction
of the matched-aperture photometry. Photometric redshifts are estimated for 143
galaxies in the 4 arcmin$^{2}$ field of overlap covered by all these data. We
confirm that strong lensing effects yield 30 images of 11 background galaxies,
of which we contribute photometric redshift estimates for three image
multiplicities. These constraints enable the construction of a revised lens
model that confirms the bimodal structure, and from which we measure a mass of
M$_{600 kpc}$=(2.36$\pm$0.23)$\times$10$^{14}$M$_{\odot}$. In parallel, new
spectroscopy using MMT/Binospec and archival data contributes thirteen galaxies
which meet our velocity and transverse radius criteria for cluster membership.
The two cluster components have a pair-wise velocity of $\lessapprox$100
kms$^{-1}$, favoring an orientation in the plane of the sky with a transverse
velocity of 100-1700 kms$^{-1}$. At the same time, the brightest cluster galaxy
is offset in velocity from the systemic mean value. New LOFAR and VLA radio
maps uncover the BCG and a large red galaxy in the northeastern side to be
head-tail galaxies, suggesting that this component has already traversed
southwestern side and is now exiting the cluster to the northeast.
