We investigate the fueling and the feedback of nuclear activity in the Seyfert 2 galaxy NGC1068, by studying the distribution and kinematics of molecular gas in the torus and its connections. We use ALMA to image the emission of a set of molecular gas tracers in the circumnuclear disk (CND) and the torus of the galaxy using the CO(2-1), CO(3-2) and HCO^+^(4-3) lines with spatial resolutions ~0.03"-0.09"(2-6pc). ALMA resolves the CND as an asymmetric ringed disk of D~400pc-size and mass of ~1.4x10^8^M_{sun}. The inner edge of the ring is associated with edge-brightened arcs of NIR polarized emission identified with the working surface of the AGN ionized wind. ALMA proves the existence of a molecular torus of M_torus ~3x10^5^M{sun}, which extends over a large range of spatial scales D=10-30pc around the central engine. The new observations evidence the density radial stratification of the torus: the HCO^+^(4-3) torus, with a full size D=11pc, is a factor of 2-3 smaller than its CO(2-1) and CO(3-2) counterparts, which have full-sizes D=26pc and D=28pc, respectively. The torus is connected to the CND through a network of gas streamers. The kinematics of molecular gas show strong departures from circular motions in the torus, the gas streamers, and the CND. These velocity distortions are interconnected and are part of a 3D outflow that reflects the effects of AGN feedback on the kinematics of molecular gas across a wide range of spatial scales. We conclude that a wide-angle AGN wind launched from the accretion disk is impacting a sizeable fraction of the gas inside the torus (~0.4-0.6xM_torus). However, a large gas reservoir (~1.2-1.8x10^5^M_{sun}_) close to the equatorial plane of the torus remains unaffected by the AGN wind and can continue fueling the AGN for ~1-4Myr. AGN fueling seems nevertheless thwarted on intermediate scales (15pc<r<50pc).

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