We present Atacama Large Millimeter/submillimeter Array [C ii] 158 mu m line and underlying far-infrared (FIR) continuum emission observations (0.'' 70 x 0.'' 56 resolution) toward HSC J124353.93+010038.5 (J1243+0100) at z = 7.07, the only low-luminosity (M (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 (FIR) = 3.5 x 10(12) L (circle dot). The spatially extended component is responsible for similar to 40% of the emission. The area-integrated [C ii] spectrum shows a broad wing (FWHM = 997 km s(-1), L ([C ii]) = 1.2 x 10(9) L (circle dot)), as well as a bright core (FWHM = 235 km s(-1), L ([C ii]) = 1.9 x 10(9) L (circle dot)). This wing is the first detection of a galactic-scale quasar-driven outflow (atomic outflow rate >447 M (circle dot) yr(-1)) at z > 7. The estimated large mass-loading factor of the total outflow (e.g., greater than or similar to 9 relative to the [C ii]-based star formation rate) 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 (similar to 3.3 x 10(10) M (circle dot)), although it is not yet spatially resolved. Finally, we found that J1243+0100 has a black hole mass-to-dynamical mass (and -to-bulge mass) ratio of similar to 0.4% (similar to 1%), consistent with the local value within the uncertainties. Our results therefore suggest that the black hole-host coevolution relation is already in place at z similar to 7 for this object.