Reducing aerodynamic noise from rotating fans while preserving their aerodynamic performance remains a major challenge in the design of low-noise flow-control and ventilation systems. Motivated by this challenge, the present study performs a comprehensive numerical investigation of the coupled aerodynamic and aeroacoustic behavior of a rotating fan equipped with straight and serrated trailing-edge blades under both quiescent and inflow operating conditions. The effects of rotational speed, external inflow, and blade trailing-edge geometry on flow structure, pressure distribution, and acoustic response are systematically examined. Simulations are conducted for two rotational speeds and two inlet conditions to isolate rotation-induced mechanisms from inflow-dominated effects governing noise generation and propagation. Aerodynamic results show that under quiescent inflow, the flow field is primarily driven by fan rotation, leading to localized acceleration, non-uniform outlet mass flow, and a strong dependence on rotational speed. The presence of external inflow leads to a more uniform flow field and increased mass flow rates, while reducing the sensitivity to trailing-edge geometry. Moreover, rotational speed emerges as the dominant factor governing both aerodynamic and acoustic responses. Trailing-edge serrations mainly affect low-frequency acoustic behavior at low rotational speeds under quiescent conditions, whereas their influence diminishes at higher speeds and in the presence of inflow. External inflow also raises baseline acoustic levels and modifies the spatial distribution of the acoustic field. Overall, the results highlight the regime-dependent effectiveness of trailing-edge serrations and underscore the importance of accounting for realistic inflow environments in the aerodynamic and aeroacoustic design of low-noise rotating machinery.