Various 2D carbons demonstrate significant effects of surface oxidation, heating, suspending–drying, cryogelation, swelling, and adsorption of polar and nonpolar compounds on the morphological, structural, and textural characteristics. Heating at 120–150 °C could result in collapse of pores not only between carbon sheets in stacks but also between neighboring stacks; therefore, the specific surface area (SSA) decreases by a factor of 30–100 for preheated graphene oxides (GO). According to the TEM and XRD data, the GO structure is rather amorphous, since only small X-ray coherent scattering regions demonstrate a certain order giving broad XRD (001) and (002) lines. In the Raman spectra, the D line (disordered defect structures with sp3 hybridized C atoms) intensity for GO is similar to that of the G line (ordered structures with sp2 hybridized C atoms). The graphite oxide (GtO) structure, which is closer to that of graphite than that of GO, is characterized by intensive G and low D lines, and the main XRD peak at 26.4° (characteristic for graphite) is broadened similar to the XRD peak of GO at 10°. Despite the GO stacks have a tendency to collapse upon heating, the collapsed stacks can be swollen not only in water (strongly) but also in liquid nitrogen (relatively weakly). Therefore, the use of GO in aqueous media can provide great SSA values in contact with the solvent and solute molecules. This could provide high efficiency of the GO use for purification of wastewater, separation of solutes, etc. MLGO produced from natural flake graphite as a precursor (flakes < 0.2 mm in size) using a modified method of ionic hydration and freeze–drying is characterized by typical light brown color, low bulk density, flexible sheet stacks easily collapsed, but its interaction with water results in strong swelling. Interaction between the carbon sheets in preheated MLGO is strong and nonpolar molecules, such as benzene, n–decane, poorly penetrate between the sheets, i.e., intercalation adsorption is small. However, water molecules can effectively penetrate (this is rather intercalation adsorption resulting in swelling) between the sheets, but the swelling effect of water adsorbed from the gas phase could be weaker than that in the aqueous suspensions. Thus, the proposed synthesis method of MLGO using natural graphite is effective and appropriate for preparation of the materials for various practical applications.