Four S-containing azo-compounds based on 1-phenyl-3-methyl-4-azopyrazole-5-one and 10 novel metal complexes of Cu(II), Co(II), and Ni(II) were isolated and identified by X-ray single crystal analysis, FTIR, 1H NMR, and UV–Vis spectroscopy. The hydrazo-forms of the organic species in a solid state and solutions were proven. Studies of proteolytic equilibria, as well as complex formation in solutions, allowed the calculation of acidity and formation constants of the complexes in ethanol aqueous solutions. The types of coordination of organic species were determined by spectroscopic analysis together with X-ray analysis of a model complex. The sulfonamide group seems not to be involved in coordination. The toxicity of the compounds was determined based on the nature of the diazo-component and increased by replacing a benzene ring with a naphthol fragment. Computer screening revealed that the studied compounds exhibited the highest likelihood of enhancing HMGSC2 expression and displayed potential as antipyretics and anti-tuberculosis agents. Additionally, their solubilities in n-hexane, 1-octanol, and phosphate buffer at pH 7.4 were assessed. These solvents serve as models of physiological fluids and possess lipophilic properties that aid in membrane penetration. Subsequently, the thermodynamic constants were calculated.