Small-scale processes can determine many aspects of the global behavior of complex plasma physical systems such as magnetically-confined toroidal plasmas, near-Earth space plasmas, and solar plasmas. Examples of this include reconnection of magnetic fields lines in narrow layers near rational magnetic surfaces, which lead to global redistribution of plasma density, current and temperature, and anomalous transport from microscopic magnetic islands and vortices. In this work the kinetic nonlinear dynamics of small-scale magnetic perturbations in a magnetized high temperature plasma is considered, including the effects of diamagnetism, ion gyroradius, finite electron mass and magnetic shear. A particle-in-cell simulation model, based on the electromagnetic gyrokinetic Vlasov-Poisson-Ampere system, is utilized to investigate the spontaneous generation of inertial-scale magnetic islands in various regimes of the plasma beta. We focus on two aspects of the physical processes related to the formation of undamped stationary propagating magnetic modes and the cross-scale coupling effects of shorter wavelength gradient-driven fluctuations on the longer wavelength magnetic fluctuations.