A self-consistent global three-dimensional kinetic study of Mercury's magnetosphere is carried out examining waves and instabilities generated by ion temperature anisotropy and plasma flow. The overall structure of Mercury's upstream bow shock and magnetosheath are qualitatively very similar to those of Earth. Beam-generated long-wavelength oscillations are present upstream of Mercury's quasi-parallel bow shock, whereas large-amplitude mirror waves develop downstream of the quasi-parallel bow shock in the magnetosheath. A train of mirror waves forms also downstream of the quasi-perpendicular bow shock. A velocity shear near the magnetopause can lead to formation of vortex-like structures. The magnetospheric cavity close to the planet's equatorial plane is filled with ions much hotter than the solar wind protons. A drift-driven plasma belt close to the equator is present in the model and contains plasma with high-temperature anisotropy, and the loss cone for charged particles in this region is large. The belt may cause diamagnetic effects superimposed on the planet's internal magnetic field and can interact with Mercury's magnetopause.