The goal of this work is measuring magneto-optical spectra of high quality graphene crystals in the terahertz and infrared regions in order to understand magneto-optical phenomena in graphene unperturbed by defects, impurities, inhomogeneities of chemical potential, etc. For this purpose we used scotch-tape exfoliated hBN-encapsulated graphene membranes suspended over circular apertures of a few dozens of microns in diameter. In order to enable measurements on such small samples, we developed a compact superconducting magnet compatible with commercial FTIR spectrometers and infrared microscopes. Our experiments revealed large magnitudes of the magneto-optical effects: magneto-absorption of circularly polarized light approaching the 50% limit valid for ultrathin conducting films, full magnetic circular dichroism, Faraday rotation angle up to 9°, as well as efficient tunability of these effects with the help of the external magnetic field. Apart form that, we also registered a number of subtle puzzling effects incompatible with a simple single-electron theory.