We present CO(2−1) and adjacent continuum observations of seven nearby radio-quiet type-2 quasars (QSO2s) obtained with ALMA at ∼0.2″ resolution (370 pc at z ∼ 0.1). These QSO2s are luminous (L_[OIII] > 10^8.5 L_⊙ ∼ M_B < −23), and their host galaxies massive (M_* ∼ 10¹¹ M_⊙). The CO morphologies are diverse, including disks and interacting systems. Two of the QSO2s are red early-type galaxies with no CO(2–1) detected. In the interacting galaxies, the central kiloparsec contains 18–25% of the total cold molecular gas, whereas in the spirals it is only ∼5–12%. J1010+0612 and J1430+1339 show double-peaked CO flux maps along the major axis of the CO disks that do not have an optical counterpart at the same angular resolution. Based on our analysis of the ionized and molecular gas kinematics and millimeter continuum emission, these CO morphologies are most likely produced by active galactic nucleus (AGN) feedback in the form of outflows, jets, and/or shocks. The CO kinematics of the QSO2s with CO(2−1) detections are dominated by rotation but also reveal noncircular motions. According to our analysis, these noncircular motions correspond to molecular outflows that are mostly coplanar with the CO disks in four of the QSO2s, and either to a coplanar inflow or vertical outflow in the case of J1010+0612. These outflows represent 0.2–0.7% of the QSO2s’ total molecular gas mass and have maximum velocities of 200–350 km s⁻¹, radii from 0.4 to 1.3 kpc, and outflow mass rates of 8–16 M_⊙ yr⁻¹. These outflow properties are intermediate between those of the mild molecular outflows measured for Seyfert galaxies and the fast and energetic outflows shown by ultra-luminous infrared galaxies. This suggests that it is not only AGN luminosity that drives massive molecular outflows. Other factors such as jet power, coupling between winds, jets, and/or ionized outflows and the CO disks, and amount or geometry of dense gas in the nuclear regions might also be relevant. Thus, although we do not find evidence for a significant impact of quasar feedback on the total molecular gas reservoirs and star formation rates, it appears to be modifying the distribution of cold molecular gas in the central kiloparsec of the galaxies.