This paper presents a comprehensive study on electric vehicle (EV) battery modelling, state estimation, and bidirectional charging infrastructure through the development of an integrated MATLAB Simscape framework. With the rapid adoption of EVs, challenges surrounding accurate battery management, reliable charging strategies, and grid stability have become increasingly critical. The research addresses these challenges by combining advanced battery modelling, Extended Kalman Filter (EKF)-based estimation, fast DC charging design, and vehicle-to-grid (V2G) interaction into a unified system. A detailed battery pack is modelled to capture electro-thermal dynamics, resistance behaviour, and degradation trends. EKF algorithms were implemented to estimate both State of Charge (SOC) and State of Health (SOH), demonstrating high accuracy and robustness against nonlinearities. At the charging system level, a fast DC charging station was designed with bidirectional power capability, enabling both grid-to-vehicle (G2V) and V2G operations. Converter design, LCL filtering, and harmonic analysis were incorporated to ensure grid compliance and efficient energy transfer. Beyond individual components, the framework was extended to evaluate grid-level implications of large-scale EV integration. Optimized charging and discharging schedules were proposed to mitigate peak demand, support renewable balancing, and minimize transformer loading, while simultaneously preserving battery longevity. Simulation results confirmed stable operation across diverse scenarios, validating the feasibility of the proposed strategies.