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.