  We present $\kappa$ Andromeda b's 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 companion's atmospheric properties and
orbit. $\kappa$ And b's 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 b's orbit with ExoSOFT using new astrometry
spanning seven years reaffirms its high eccentricity ($0.77\pm0.08$). 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.
