This thesis presents the experimental studies of the magnetic and hyperfine interaction properties of four novel Fe-based superconductors (ThFeAsN, CsEuFe4As4, Rb1-δEuFe4As4, and EuFe0.97Ni0.03As2) and one new non-superconducting compound (EuFeAs2). It is supplemented by ab-initio calculations of the electronic structure and magnetism of the three superconductors. The experimental studies are based on the results of x-ray diffraction, magnetic susceptibility, magnetization, and 57Fe and 151Eu Mössbauer spectroscopy measurements. The superconductor ThFeAsN crystallizes in the tetragonal space group P4/nmm with the lattice parameters a = 4.0356(1) Å and c = 8.5286(1) Å. It is shown that there is no magnetic order of the Fe magnetic moments down to 2.0 K. We suggest that nonappearance of Fe magnetism in ThFeAsN may be because of an internal uniaxial chemical pressure whose presence is manifested by the unusually small c/a ratio. We provide theoretical evidence for a mixture of ionic and covalent chemical bonding and metallic characteristics. We present a detailed analysis of the calculated energy band structure of ThFeAsN. A quadrupole doublet well describes the shape of the Mössbauer spectra with a small quadrupole splitting that increases with lowering temperature. Good agreement is found between the calculated and extrapolated 0 K quadrupole splitting values. A fair agreement is noted between the experimental Debye temperature 332(2) K and 370 K of the calculated one. We show that the superconductor CsEuFe4As4 crystallizes in the tetragonal space group P4/mmm with the lattice parameters a = 3.8956(1) Å and c = 13.6628(5) Å. We show that the Fe atoms carry no magnetic moment down to 2.1 K and that the ferromagnetic order is related to the Eu magnetic moments. We establish that the Curie temperature Tc = 15.97(8) K found from the temperature dependence of the hyperfine magnetic field at 151Eu nuclei is well-matched with the temperature dependence of the transferred hyperfine magnetic field at 57Fe nuclei that is produced by the ferromagnetically ordered Eu sublattice. The magnetic moments of the Eu atoms are shown to be perpendicular to the crystallographic c-axis. The T 3⁄2 power-law perfectly describes the temperature dependence of the principal component of the electric field gradient tensor, both at Fe and Eu sites. The calculated and the measured parameters of the hyperfine-interaction are in excellent agreement with each other. We determine that the Debye temperature of CsEuFe4As4 is 295(3) K. Ab-initio calculations suggest a mixture of ionic, covalent, and metallic bonding between the constituent atoms in the CsEuFe4As4 superconductor. We confirm that the strongly localized Eu f states are the origin of the magnetic moment of CsEuFe4As4, in agreement with the experimental results. We show that an almost zero magnetic moment carried by the Fe atoms is caused by the spin-up and spin-down states' apparent symmetry. We show that the Fermi surfaces have hole-like and electron-like pockets located at the center and corners of the Brillouin zone, respectively. The superconductor Rb1-δEuFe4As4 crystallizes in the tetragonal space group P4/mmm with the lattice parameters a = 3.8849(1) Å and c = 13.3370(3) Å. We show that the Fe atoms carry no magnetic moment down to 2.1 K and that the ferromagnetic order is associated solely with the Eu magnetic moments. The Curie temperature Tc = 16.54(8) K is found from the temperature dependence of both the hyperfine magnetic field at 151Eu nuclei and the transferred hyperfine magnetic field at 57Fe nuclei induced by the ferromagnetically ordered Eu sublattice. We find that the Eu magnetic moments lie in the ab plane. It is observed that the temperature dependence of the principal component of the electric field gradient tensor, at both Fe and Eu sites, is well described by a T3⁄2 power-law relation. There is good agreement between the calculated and measured parameters of the hyperfine-interaction. We determine that the Debye temperature of Rb1-δEuFe4As4 is 391(8) K. Ab-initio calculations indicate the presence of a mixture of ionic, covalent, and metallic bonding between the constituent atoms in the RbEuFe4As4 superconductor. We show that the magnetic moment of RbEuFe4As4 is mainly a result of the strongly localized Eu f states. It is shown that an almost zero magnetic moment carried by the Fe atoms originates from an apparent symmetry of the spin-up and spin-down states. We show that the electrical and chemical properties of RbEuFe4As4 are closely associated with the presence of the Fe 3d states in the Fermi energy region. The Fermi surfaces display hole-like and electron-like pockets, respectively, at the center and corners of the Brillouin zone. We find that in both the EuFeAs2 compound and 14 K superconductor EuFe0.97Ni0.03As2 the antiferromagnetic ordering of the Fe sublattice is of a spin-density-wave type with the Néel temperatures and Fe saturation magnetic moments of 106.2(1.9) K, 0.78(1) μB and 56.6(2.2) K, 0.47(1) μB, respectively. We show that the Néel temperatures and the saturation hyperfine magnetic fields in the two compounds with the antiferromagnetically ordered Eu sublattice are 44.4(5) K, 294.2(7) kOe and 43.5(1) K, 290.5(1) kOe respectively. The 3% substitution of Fe by Ni in EuFeAs2, aside from producing superconductivity in EuFe0.97Ni0.03As2, radically reduces the strength of magnetism of the Fe sublattice and has nearly no impact on the magnetism of the Eu sublattice. The appearance of antiferromagnetically ordered Fe and Eu sublattices in EuFe0.97Ni0.03As2 verifies that superconductivity and magnetism coexist in this compond. The growth of the magnitude of the main component of the electric field gradient tensor, at both Fe and Eu sites, with reducing temperature, is well described by a T3⁄2 power-law relation. We determine the Debye temperatures of EuFeAs2, EuFe0.97Ni0.03As2, and the FeAs2 impurity phase to be 355(18), 428(14), and 594(25) K, respectively. In summary, for all of the studied compounds, there is no magnetic ordering associated with iron sub-lattices in the ThFeAsN, CsEuFe4As4, and Rb1-δEuFe4As4 compounds. The iron sublattice is magnetically ordered in the EuFeAs2 and the EuFe0.97Ni0.03As2 superconductor. There is a coexistence of magnetism and superconductivity associated with europium in the CsEuFe4As4, Rb1-δEuFe4As4, EuFe0.97Ni0.03As2 compounds. There is a good agreement between the calculated and the measured hyperfine and magnetic parameters for most studied compounds.