Linear and non-linear dynamics of di erent electrostatic modes is studied in inhomoge- neous, magnetized and non-Maxwellian plasmas. A linear dispersion relation is obtained for the Ion Temperature Gradient (ITG) mode and numerically analyzed in the presence of dust charge uctuations and Kappa distributed electrons. It is found that these nonthermal pop- ulations reduce the growth rate ITG. It is also noticed that the characteristics of ITG driven vortices change with the value of spectral index, inhomogeneities, scale lengths and dust charge uctuations. Electron Temperature Gradient (ETG) mode is investigated in a collisionless plasma with Kappa distributed ions. Di erent aspects of the ETG-mode are discussed and noticed that these are modi ed with the superthermality e ect of ions e.g., the phase velocity of the ETG- mode. In the nonlinear regime, we found the ETG mode driven vortex structures, where we noticed that the vortex speed and the amplitude changes with the Kappa value and the ion to electron temperature ratio. Further, the ETG mode is discussed by including the parallel electron dynamics. It is noticed that the parallel motion of electrons stabilizes the ETG instability. Thus the possibility of the formation of nonlinear vortex structures increase. These investigations are discussed both for circular and elliptic type dipolar vortices. In this model an eigen mode dispersion relation is also obtained in the ballooning limit. This relation is also modi ed in the presence of non- Maxwellian ions. Electron AcousticWaves (EAW) are studied with non-Maxwellian hot electrons and stationary/non- stationary ions. In this investigation, both the linear and nonlinear propagation of EAW with stationary and non-stationary ions are discussed. It is noticed that the behavior of EAW is di erent for Kappa distributed hot electrons and Cairn''s distributed hot electrons. Superthermality e ect of electrons and ions on the dust charge uctuations and on the low frequency dust drift/acoustic waves is investigated in an inhomogeneous dusty plasma. It is noticed that this superthermality e ect of ions and electrons reduces the growth rate of the instability due to dust charge uctuations. It is found that dust charge and the superthermalty e ect of ion and electrons reduce the growth rate of instability. In the nonlinear regime, the condition for the existence of dust drift/ acoustic wave driven vortices modi es due to spectral index Kappa. Further, we have investigated the ITG driven solitons and shocks for the electron-ion plasmas for thest time. In this case, it is noticed that the amplitude of the soliton decreases and width of the soliton increases with the increase in ion temperature. In the case of dissipated electron- ion plasmas, the amplitude of the shock increases for with an increase in thei value.