NGC 4945 is one of the nearest (D ≈ 3.8 Mpc; 1″ ≈ 19 pc) starburst galaxies. To investigate the structure, dynamics, and composition of the dense nuclear gas of this galaxy, ALMA band 3 (λ ≈ 3−4 mm) observations were carried out with ≈2″ resolution. Three HCN and two HCO+ isotopologues, CS, C3H2, SiO, HCO, and CH3C2H were measured. Spectral line imaging demonstrates the presence of a rotating nuclear disk of projected size 10″ × 2″ reaching out to a galactocentric radius of r ≈ 100 pc with position angle PA = 45° ± 2°, inclination i = 75° ± 2° and an unresolved bright central core of size ≲2″. The continuum source, representing mostly free-free radiation from star forming regions, is more compact than the nuclear disk by a linear factor of two but shows the same position angle and is centered 0.′′39 ± 0.′′14 northeast of the nuclear accretion disk defined by H2O maser emission. Near the systemic velocity but outside the nuclear disk, both HCN J = 1 → 0 and CS J = 2 → 1 delineate molecular arms of length ≳15″ (≳285 pc) on opposite sides of the dynamical center. These are connected by a (deprojected) ≈ 0.6 kpc sized molecular bridge, likely a dense gaseous bar seen almost ends-on, shifting gas from the front and back side into the nuclear disk. Modeling this nuclear disk located farther inside (r ≲100 pc) with tilted rings provides a good fit by inferring a coplanar outflow reaching a characteristic deprojected velocity of ≈50 km s−1. All our molecular lines, with the notable exception of CH3 C2H, show significant absorption near the systemic velocity (≈571 km s−1), within the range ≈500–660 km s−1. Apparently, only molecular transitions with low critical H2 density (ncrit ≲ 104 cm−3) do not show absorption. The velocity field of the nuclear disk, derived from CH3 C2H, provides evidence for rigid rotation in the inner few arcseconds and a dynamical mass of Mtot = (2.1 ± 0.2) × 108 M⊙ inside a galactocentric radius of 2.′′45 (≈45 pc), with a significantly flattened rotation curve farther out. Velocity integrated line intensity maps with most pronounced absorption show molecular peak positions up to ≈1.′′5 (≈30 pc) southwest of the continuum peak, presumably due to absorption, which appears to be most severe slightly northeast of the nuclear maser disk. A nitrogen isotope ratio of 14N/15N ≈ 200–450 is estimated. This range of values is much higher then previously reported on a tentative basis. Therefore, because 15N is less abundant than expected, the question for strong 15N enrichment by massive star ejecta in starbursts still remains to be settled.