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We present ALMA ~0.02"-resolution observations of the nucleus of the nearby (~14 Mpc) type-2 AGN NGC 1068 at HCN/HCO+/HNC J=3-2 lines, as well as at their 13C isotopologue and vibrationally excited lines, to scrutinize the morphological/dynamical/chemical/physical properties of dense molecular gas in the putative dusty molecular torus around a mass-accreting supermassive black hole. We confirm almost east-west-oriented dense molecular gas emission both morphologically and dynamically, which we regard as coming from the torus. Bright emission is compact (<3 pc), and low-surface-brightness emission extends out to 5-7 pc. These dense molecular gas properties are not symmetric between the eastern and western torus. The HCN J=3-2 emission is stronger than the HCO+ J=3-2 emission within the ~7 pc torus region, with an estimated dense molecular mass of (0.4-1.0)x10^6Msun. We interpret that HCN abundance is enhanced in the torus. We detect signatures of outflowing dense molecular gas and a vibrationally excited HCN J=3-2 line. Finally, we find that in the innermost (<1 pc) part of the torus, the dense molecular line rotation velocity, relative to the systemic velocity, is the opposite of that in the outer (>2 pc) part, in both the eastern and western torus. We prefer a scenario of counter-rotating dense molecular gas with innermost almost-Keplerian-rotation and outer slowly rotating (far below Keplerian) components. Our high-spatial-resolution dense molecular line data reveal that torus properties of NGC 1068 are much more complicated than the simple axi-symmetrically rotating torus picture in the classical AGN unification paradigm.