This study proposes a new method to improve the accuracy of car-following models in predicting the mobility of mixed traffic flow involving trucks and automated vehicles (AVs). A classification is developed to categorize car-following behaviors into eight distinct modes based on vehicle type (passenger car/truck) and autonomy level (human-driven vehicle [HDV]/AV) for parameter calibration and simulation. The car-following model parameters are calibrated based on the HighD dataset, and the models are selected through minimizing statistical error. A cellular-automaton-based simulation platform is implemented in MATLAB (R2023b), and a decision framework is developed for the simulation. Key findings demonstrate that mode-specific parameter calibration improves model accuracy, achieving an average error reduction of 80% compared to empirical methods. The simulation results reveal a positive correlation between the AV penetration rate and traffic flow stability, which consequently enhances capacity. Specifically, a full transition from 0% to 100% AV penetration increases traffic capacity by 50%. Conversely, elevated truck penetration rates degrade traffic flow stability, reducing the average speed by 75.37% under full truck penetration scenarios. Additionally, higher AV penetration helps stabilize traffic flow, leading to reduced speed fluctuations and lower emissions, while higher truck proportions contribute to higher emissions due to increased traffic instability.