Shared autonomous electric vehicles (SAEVs) are predicted to become a significant solution to reduce global emissions and energy consumption resulting from urban transportation. The centralized operation of SAEVs not only allows large-scale travel demand response but also can provide essential ancillary services to the smart grid through the concept of vehicle-to-grid (V2G). With V2G technology, unused electric vehicles can work as a distributed energy storage facility for the electricity grid to smoothen the intermittent demand. Designing and operating a V2G-enabled SAEV system is challenging. This problem involves complicated planning and operational decisions, as well as time-varying electric tariffs. In this work, a flow-based Integer Linear Programming (ILP) model is formulated for determining the optimal configurations (charging infrastructure and fleet size) and daily operation strategies (serving passengers, relocation, charging/discharging). The developed mathematical model allows for maximizing the total profit, comprising investment cost, revenue from serving passengers, and V2G profit through charging/discharging schedules. A two-stage Benders decomposition-based algorithm is proposed to address the sophisticated ILP problem. Via testing instances in the Manhattan network based on real-world and synthetic data, we have demonstrated the feasibility of our approaches and studied the benefits of integrating V2G in the SAEV system.