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The generation of magnetohydrodynamic (MHD) waves and their instabilities are studied in galactic gaseous rotating plasmas with the effects of the magnetic field, the self gravity, the diffusion-convection of cosmic rays as well as the gas and cosmic-ray pressures. The coupling of the Jeans, Alfv{\'e}n and magnetosonic waves, and the conditions of damping or instability are studied in three different cases, namely when the propagation direction is perpendicular, parallel and oblique to the static magnetic field, and are shown to be significantly modified by the effects of the Coriolis force due to the rotation of cosmic fluids and the cosmic-ray diffusion. The coupled modes can be damped or anti-damped depending on the wave number is above or below the Jeans critical wave number that is reduced by the effects of the Coriolis force and the cosmic-ray pressure. It is found that the deviation of the axis of rotation from the direction of the static magnetic field gives rise to the coupling between the Alfv{\'e}n wave and the classical Jeans mode which otherwise results into the modified slow and fast Alfv{\'e}n waves as well as the modified classical Jeans modes. Furthermore, due to the effects of the cosmic rays diffusion, there appears a new wave mode (may be called the fast Jeans mode) in the intermediate frequency regimes of the slow and fast Alfv{\'e}n waves, which seems to be dispersionless in the long-wavelength propagation and has a lower growth rate of instability in the high density regimes of galaxies. The dispersion properties and the instabilities of different kinds of MHD waves reported here can play pivotal roles in the formation of various galactic structures at different length scales., Comment: 11 pages, 5 figures