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We present continuum and molecular line emission ALMA observations of OH 231.8+4.2, a well studied bipolar nebula around an asymptotic giant branch (AGB) star. The high-angular resolution (∼0.2"-0.3") and sensitivity of our ALMA maps provide the most detailed and accurate description of the overall nebular structure and kinematics of this object to date. We have identified a number of outflow components previously unknown. Species studied in this work include ¹²CO, ¹³CO, CS, SO, SO₂, OCS, SiO, SiS, H₃O⁺, Na³⁷Cl, and CH₃OH. The molecules Na³⁷Cl and CH₃OH are first detections in OH 231.8+4.2, with CH₃OH being also a first detection in an AGB star. Our ALMA maps bring to light the totally unexpected position of the mass-losing AGB star (QX Pup) relative to the large-scale outflow. QX Pup is enshrouded within a compact (≤60AU) parcel of dust and gas (clump S) in expansion (V_exp∼5-7km/s) that is displaced by ∼0.6" to the south of the dense equatorial region (or waist) where the bipolar lobes join. Our SiO maps disclose a compact bipolar outflow that emerges from QX Pup's vicinity. This outflow is oriented similarly to the large-scale nebula but the expansion velocities are about ten times lower (V_exp≤35km/s). We deduce short kinematical ages for the SiO outflow, ranging from ∼50-80yr, in regions within ∼150AU, to ∼400-500yr at the lobe tips (∼3500AU). Adjacent to the SiO outflow, we identify a small-scale hourglass-shaped structure (mini-hourglass) that is probably made of compressed ambient material formed as the SiO outflow penetrates the dense, central regions of the nebula. The lobes and the equatorial waist of the mini-hourglass are both radially expanding with a constant velocity gradient (V_exp∝r). The mini-waist is characterized by extremely low velocities, down to ∼1km/s at ∼150AU, which tentatively suggest the presence of a stable structure. The spatio-kinematics of the large-scale, high-velocity lobes (HV lobes), and the dense equatorial waist (large waist) known from previous works are now precisely determined, indicating that both were shaped nearly simultaneously about ∼800-900yr ago. We report the discovery of two large (∼8"x6"), faint bubble-like structures (fish bowls) surrounding the central parts of the nebula. These are relatively old structures, although probably slightly (∼100-200yr) younger than the large waist and the HV lobes. We discuss the series of events that may have resulted in the complex array of nebular components found in OH 231.8+4.2 as well as the properties and locus of the central binary system. The presence of ≤80yr bipolar ejections indicate that the collimated fast wind engine is still active at the core of this outstanding object.