Uncovering the structure and kinematics of the ionized core of M\,2-9 with ALMA

We present interferometric observations at 1 and 3\,mm with the Atacama Large Millimeter Array (ALMA) of the free-free continuum and mm-wavelength recombination line (mRRL) emission of the ionized core (within $\lsim$130\,au) of the young Planetary Nebula (PN) candidate M\,2-9.These inner regions are concealed in the vast majority of similar objects. A spectral index for the mm-to-cm continuum of $\sim$0.9 indicates predominantly free-free emission from an ionized wind, with a minor contribution from warm dust. The mm-continuum emission in M\,2-9 reveals an elongated structure along the main symmetry axis of the large-scale bipolar nebula with a C-shaped curvature surrounded by a broad-waisted component. This structure is consistent with an ionized bent jet and a perpendicular compact dusty disk. The presence of a compact equatorial disk (of radius $\sim$50\,au) is also supported by red-shifted CO and \trecem\ absorption profiles observed from the base of the receding north lobe against the compact background continuum. The redshift observed in the CO absorption profiles likely signifies gas infall movements from the disk toward a central source. The mRRLs exhibit velocity gradients along the axis, implying systematic expansion in the C-shaped bipolar outflow. The highest expansion velocities ($\sim$80\,\kms) are found in two diagonally opposed compact regions along the axis, referred to as the high-velocity spots/shells (HVS), indicating either rapid wind acceleration or shocks at radial distances of $\sim$0\farc02-0\farc04 ($\sim$15-25\,au) from the center. A subtle velocity gradient perpendicular to the lobes is also found, suggestive of rotation. Our ALMA observations detect increased brightness and broadness in the mRRLs... (abridged).