Reconfigurable intelligent surface (RIS)-aided terahertz (THz)-band communications are promising enablers for future wireless networks. However, array densification at high frequencies introduces significant challenges in accurate channel modeling and estimation, particularly with THz-specific fading, mutual coupling (MC), spatial correlation, and near-field effects. In this work, we model THz outdoor small-scale fading channels using the mixture gamma (MG) distribution, considering absorption losses, spherical wave propagation, MC, and spatial correlation across large base stations and RISs. We derive the distribution of the cascaded RIS-aided channel and investigate linear channel estimation techniques, analyzing the impact of various channel parameters. Numerical results based on precise THz parameters reveal that accounting for spatial correlation, MC, and near-field modeling substantially enhances estimation accuracy, especially in ultra-massive arrays and short-range scenarios. These results underscore the importance of incorporating these effects for precise, physically consistent channel modeling.