Surface semi-geostrophic turbulence is examined in this study. In our simulations, the strength of the ageostrophic component of the flows is controlled by the Rossby number ε, varying from 0.01 to 0.2. The flows manifest a cyclone-anticyclone asymmetry with a cyclonic preference for cold vortices and an anticyclonic preference for warm filaments. This asymmetry becomes especially pronounced in the flows with large ε, where an abundance of warm filaments is observed. Strong vertical motions concentrate in the small-scale filaments and at the periphery of the vortices. There, the lateral divergence becomes significant. A negative correlation between the divergence and the relative vorticity is identified using joint probability density functions. Slopes of the kinetic and potential energy spectra vary between -2.2 and -1.7 at intermediate scales. Analyses of spectral fluxes demonstrate an inverse kinetic energy cascade and a forward cascade of potential energy. As ε increases, the filaments become more numerous in the flows. They wrap around cyclones, weakening their interactions and subsequent mergers, thus suppressing the inverse cascade of kinetic energy. We characterize lateral dispersion in the SSG flows using the finite-scale Lyapunov exponents (FSLEs). They are used to identify Lagrangian coherent structures, such as those created by the interaction of vortices. The FSLEs are also used to investigate the regimes of dispersion at different scales. The results show a smooth transition from hyper-ballistic diffusion at small scales to normal diffusion at large scales.