Recent observations have revealed various structures within the gravitational influence of Sgr A* – the massive black hole in the Galactic center. These structures apparently defy the fundamental principles of star formation and stellar dynamics. On one hand, the red giants display a flat density profile, contrary to the cuspy one predicted by conventional stellar relaxation. On the other, Wolf-Rayet and OB stars are observed where in-situ star formation should have been prohibited by the strong tidal force from Sgr A*, and their spatial and phase-space distributions also contradict our understanding of stellar dynamics. To explain each of these inconsistencies, many scenarios have been proposed, which render the model increasingly complicated. Here, we suggest that the sub-parsec stellar disk surrounding Sgr A*, which was recently discovered, can reconcile all the above inconsistencies. We show that during the fragmenting past of this disk, the star-forming clumps could efficiently deplete red giants by repeatedly colliding with them. We also show that because of the torque exerted by the disk, stars within the central arcsec from Sgr A* would quickly mix in the angular-momentum space, which naturally explains the observed distributions of Wolf-Rayet and OB stars. Our results imply that Sgr A* was fueled by gas and stars several millions years ago and could have been an energetic AGN. We discuss future observations that can further testify our model.