By using unsymmetrical pyrazine- and pyrimidine-modulated oligo-α-pyridylamine ligand N-(4-methylpyrimidin-2-yl)pyrazin-2-amine (Hmpmpza) (1), 1D copper(II) coordination polymer {[Cu(mpmpza)(CH3COO)](CH3OH)(H2O)}n (2) and mononuclear copper(II) complex [Cu(Hmpmpza)(NO3)2] (3) were first successfully synthesized and structurally characterized. In complex (2), Cu(II) is six-coordinated in an elongated octahedral geometry. The Hmpmpza molecule coordinates with the Cu(II) as a tridentate ligand, in which the pyrimidine and amine group nitrogen atoms link the coordination units to an infinite 1-D chain polymer. Extensive hydrogen bonds between amino groups, acetate anions, methanol, and water molecules are observed in 2, resulting in a 3D network of the 2. Complex 2 provides the first example of the complex with a modulated Hdpa ligand, in which nitrogen atoms both of the pyrazine and pyrimidine cycles participated in the coordination with the metal center. There are two crystallographically independent molecules in a mononuclear complex 3 and the Cu(II) atom is six-coordinated in an elongated octahedral geometry. Hmpmpza in complex 3 coordinates to the Cu(II) in an anti-anti conformation as a bidentate ligand. The hydrogen bonds between amino groups and coordinated nitrate anions in complex 3, link its molecules to a 1-D chain structure. However, no hydrogen bonding linkage between the 1-D chains is observed. The temperature dependence magnetic susceptibility measurement for complex 2 described by the Bonner-Fischer approximation shows a weak antiferromagnetic coupling between Cu(II) ions. The best fitting results were obtained with parameters g = 2.141, J = −0.73 cm−1 and R = 4.85 × 10−6. The molecular dynamics (MD) simulations of the 2-hAChE, 3-hAChE, 2-hBChE, and 3-hBChE complexes offer comprehensive insights into the stability and dynamic behavior of ligand-protein interactions. These findings contribute to a detailed understanding of the specific dynamics governing the stability of acetylcholinesterase and butyrylcholinesterase complexes.