We present $kappa$ Andromeda bs photometry and astrometry taken with Subaru/SCExAO+HiCIAO and Keck/NIRC2, combined with recently published SCExAO/CHARIS low-resolution spectroscopy and published thermal infrared photometry to further constrain the companions atmospheric properties and orbit. $kappa$ And bs Y/Y-K colors are redder than field dwarfs, consistent with its youth and lower gravity. Empirical comparisons of its Y-band photometry and CHARIS spectrum to a large spectral library of isolated field dwarfs reaffirm the conclusion from Currie et al. (2018) that it likely has a low gravity but admit a wider range of most plausible spectral types (L0-L2). Our gravitational classification also suggests that the best-fit objects for $kappa$ And b may have lower gravity than those previously reported. Atmospheric models lacking dust/clouds fail to reproduce its entire 1--4.7 $mu m$ spectral energy distribution, cloudy atmosphere models with temperatures of $sim$ 1700--2000 $K$ better match $kappa$ And b data. Most well-fitting model comparisons favor 1700--1900 $K$, a surface gravity of log(g) $sim$ 4--4.5, and a radius of 1.3--1.6,$R_{rm Jup}$; the best-fit model (DRIFT-Phoenix) yields the coolest and lowest-gravity values: $T_{rm eff}$=1700 K and $log g$=4.0. An update to $kappa$ And bs orbit with ExoSOFT using new astrometry spanning seven years reaffirms its high eccentricity ($0.77pm0.08$). We consider a scenario where unseen companions are responsible for scattering $kappa$ And b to a wide separation and high eccentricity. If three planets, including $kappa$ And b, were born with coplanar orbits and one of them was ejected by gravitational scattering, a potential inner companion with mass $gtrsim10M_{rm Jup}$ could be located at $lesssim$ 25 au.
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