Aims: We investigate the fueling and the feedback of star formation and nuclear activity in NGC 1068, a nearby (D = 14 Mpc) Seyfert 2 barred galaxy, by analyzing the distribution and kinematics of the molecular gas in the disk. We aim to understand if and how gas accretion can self-regulate. Methods: We have used the Atacama Large Millimeter Array (ALMA) to map the emission of a set of dense molecular gas (n(H2) ≃ 105 - 6 cm-3) tracers (CO(3-2), CO(6-5), HCN(4-3), HCO+(4-3), and CS(7-6)) and their underlying continuum emission in the central r ~ 2 kpc of NGC 1068 with spatial resolutions ~0.3″ - 0.5″ (~20-35 pc for the assumed distance of D = 14 Mpc). Results: The sensitivity and spatial resolution of ALMA give an unprecedented detailed view of the distribution and kinematics of the dense molecular gas (n(H2) ≥ 105 - 6cm-3) in NGC 1068. Molecular line and dust continuum emissions are detected from a r ~ 200 pc off-centered circumnuclear disk (CND), from the 2.6 kpc-diameter bar region, and from the r ~ 1.3 kpc starburst (SB) ring. Most of the emission in HCO+, HCN, and CS stems from the CND. Molecular line ratios show dramatic order-of-magnitude changes inside the CND that are correlated with the UV/X-ray illumination by the active galactic nucleus (AGN), betraying ongoing feedback. We used the dust continuum fluxes measured by ALMA together with NIR/MIR data to constrain the properties of the putative torus using CLUMPY models and found a torus radius of 20+6-10pc. The Fourier decomposition of the gas velocity field indicates that rotation is perturbed by an inward radial flow in the SB ring and the bar region. However, the gas kinematics from r ~ 50 pc out to r ~ 400 pc reveal a massive (Mmol~ 2.7+0.9-1.2 × 107 M⊙) outflow in all molecular tracers. The tight correlation between the ionized gas outflow, the radio jet, and the occurrence of outward motions in the disk suggests that the outflow is AGN driven. Conclusions: The molecular outflow is likely launched when the ionization cone of the narrow line region sweeps the nuclear disk. The outflow rate estimated in the CND, dM/dt~ 63+21-37 M⊙ yr-1, is an order of magnitude higher than the star formation rate at these radii, confirming that the outflow is AGN driven. The power of the AGN is able to account for the estimated momentum and kinetic luminosity of the outflow. The CND mass load rate of the CND outflow implies a very short gas depletion timescale of ≤1 Myr. The CND gas reservoir is likely replenished on longer timescales by efficient gas inflow from the outer disk. Based on observations carried out with ALMA in Cycle 0.