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We report the results of X-ray diffraction and 57Fe Mossbauer spectroscopy study, complemented by ab-initio calculations of the electronic structure, hyperfine-interaction parameters, and elastic properties of the new 30 K superconductor ThFeAsN. The superconductor crystallizes in the tetragonal space group P4/nmm with the lattice parameters a = 4.0356(1) A and c = 8.5286(1) A. Contrary to the claims in the literature, we demonstrate unequivocally that there is no magnetic order of the Fe magnetic moments down to 2.0 K. It is suggested that the absence of Fe magnetism may be due to an internal uniaxial chemical pressure whose presence is manifested by the unusually small c/a ratio. Evidence is provided for the presence of a mixture of ionic and covalent chemical bonding and of metallic characteristics. A detailed analysis of the energy band structure of ThFeAsN is presented. The shape of the Mossbauer spectra is accounted for by a quadrupole doublet with a small quadrupole splitting that increases with decreasing temperature. Excellent agreement between the calculated and measured 0 K quadrupole splittings is observed. Fair agreement between the experimental Debye temperature of 332(2) K and the calculated one of 370 K is observed.