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We report on Atacama Large Millimeter Array (ALMA) observations of CO(3-2) emission in the Seyfert2/starburst galaxy NGC1808, at a spatial resolution of 4pc. Our aim is to investigate the morphology and dynamics of the gas inside the central 0.5kpc and to probe the nuclear feeding and feedback phenomena. We discovered a nuclear spiral of radius 1"=45pc. Within it, we found a decoupled circumnuclear disk or molecular torus of a radius of 0.13"=6pc. The HCN(4-3) and HCO$\rm^+$(4-3) and CS(7-6) dense gas line tracers were simultaneously mapped and detected in the nuclear spiral and they present the same misalignment in the molecular torus. At the nucleus, the HCN/HCO$^+$ and HCN/CS ratios indicate the presence of an active galactic nucleus (AGN). The molecular gas shows regular rotation, within a radius of 400pc, except for the misaligned disk inside the nuclear spiral arms. The computations of the torques exerted on the gas by the barred stellar potential reveal that the gas within a radius of 100pc is feeding the nucleus on a timescale of five rotations or on an average timescale of ~60Myr. Some non-circular motions are observed towards the center, corresponding to the nuclear spiral arms. We cannot rule out that small extra kinematic perturbations could be interpreted as a weak outflow attributed to AGN feedback. The molecular outflow detected at $\geqslant$250pc in the NE direction is likely due to supernovae feedback and it is connected to the kpc-scale superwind.