We present ALMA 230 GHz continuum and CO(2─1) observations of the nearby Compton-thick Seyfert galaxy ESO428─G14, with angular resolution 0"7 (78 pc). CO(2─1) is distributed in clumpy spiral arms, a lopsided circumnuclear ring (CNR) with ∼200 pc radius, and a transverse gas lane with size dyn = 5 × 109 M☉ within ∼1 kpc. We detect off-plane gas motions with respect to the main disk plane which likely trace a molecular outflow with rate ${\dot{M}}_{\mathrm{of}}\approx 0.1\mbox{--}0.3\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ , along a biconical structure with radius 700 pc. The CO outflow smoothly joins the warm molecular outflow detected in SINFONI/Very Large Telescope data in the central 170 pc, suggesting that the outflow may cool with increasing distance. Our dynamical modeling of the inner 100 pc region suggests a warped disk or bar, and of fast gas streams which may trace an inflow toward the AGN. The inner warped disk overlaps with the most obscured, CT region seen in X-rays. There, we derive a column density $N({{\rm{H}}}_{2})\approx 2\times {10}^{23}\,{\mathrm{cm}}^{-2}$ , suggesting that molecular gas may contribute significantly to the AGN obscuration. Most of the hard X-ray emitting nuclear region is deprived of cold molecular gas and shows a CO-cavity. The CO-cavity is filled with warm molecular gas traced by H2, confirming that the 3─6 keV continuum and Fe Kα emission are due to scattering from dense ISM clouds.
