Biochar is a carbon-rich material that has recently received attention due to its increasing agronomical potential. The agricultural utilization of biochar relates to its potential to act in the soil as a soil conditioner; nevertheless, complex information on the direct dependence of biochar’s physical properties (texture, particle size) and corresponding leaching and availability of organic molecules (e.g., the polycyclic and heterocyclic organic compounds) and inorganic mineral salts (based on micro- and macroelements) is still inconsistent. Multi-elemental analysis by using inductively coupled plasma atomic emission spectroscopy (ICP-OES) was used to assess the information on the contents and availability of macro- and microelements in studied commercial biochar samples. The results showed a statistically significant indirect relation between an increase in the size fraction of biochar and the content of aqueous-extractable K and Na and the direct relation with the aqueous-extractable Ca, Mg, and P. Compared to the macroelements, the detected contents of aqueous-extractable microelements were almost three orders lower, and the dependence on fraction size was not consistent or statistically significant. In addition, gas chromatography (GC) coupled with mass spectroscopy (MS) was further used to reveal the concentrations of available polycyclic aromatic and heterocyclic compounds in biochar samples. The detected concentrations of these types of organic compounds were far below the certified limits, and a statistically significant indirect correlation with particle size was also observed for all the studied biochar samples. The proposed methodological concept could provide the necessary insights into the description of biochar mineral content and its connection to biochar texture, the physicochemical properties, and the potential of biochar to release nutrients into the soil. These findings could help in the further assessment of biochar as a soil conditioner in modern agriculture.