  We present ALMA [CII] 158 $\mu$m line and underlying far-infrared (FIR)
continuum emission observations ($0''.70 \times 0''.56$ resolution) toward HSC
J124353.93$+$010038.5 (J1243$+$0100) at $z = 7.07$, the only low-luminosity
($M_{\rm 1450} > -25$ mag) quasar currently known at $z > 7$. The FIR continuum
is bright (1.52 mJy) and resolved with a total luminosity of $L_{\rm FIR} = 3.5
\times 10^{12}~L_\odot$. The spatially extended component is responsible for
$\sim 40\%$ of the emission. The area-integrated [CII] spectrum shows a broad
wing (${\rm FWHM} = 997$ km s$^{-1}$, $L_{\rm [CII]} = 1.2 \times
10^9~L_\odot$) as well as a bright core (${\rm FWHM} = 235$ km s$^{-1}$,
$L_{\rm [CII]} = 1.9 \times 10^9~L_\odot$). This wing is the first detection of
a galactic-scale quasar-driven outflow (atomic outflow rate $> 447~M_\odot$
yr$^{-1}$) at $z > 7$. The estimated large mass loading factor of the total
outflow (e.g., $\gtrsim 9$ relative to the [CII]-based SFR) suggests that this
outflow will soon quench the star-formation of the host. The core gas dynamics
are governed by rotation, with a rotation curve suggestive of a compact bulge
($\sim 3.3 \times 10^{10}~M_\odot$), although it is not yet spatially resolved.
Finally, we found that J1243$+$0100 has a black hole mass-to-dynamical mass
ratio (and -to-bulge mass ratio) of $\sim 0.4\%$ ($\sim 1\%$), consistent with
the local value within uncertainties. Our results therefore suggest that the
black hole-host co-evolution relation is already in place at $z \sim 7$ for
this object.
