As we move towards a mixed-traffic scenario of Autonomous vehicles (AVs) and Human-driven vehicles (HDVs), understanding the car-following behaviour is important to improve traffic efficiency and road safety. Using a real-world trajectory dataset, this study uses descriptive and statistical analysis to investigate the car-following behaviours of three vehicle pairs: HDV-AV, AV-HDV and HDV-HDV in mixed traffic. The ANOVA test showed that car-following behaviours across different vehicle pairs are statistically significant (p-value < 0.05). We also introduce a data-driven Knowledge Distillation Neural Network (KDNN) model for predicting car-following behaviour in terms of speed. The KDNN model demonstrates comparable predictive accuracy to its teacher network, a Long Short-Term Memory (LSTM) network, and outperforms both the standalone student network, a Multilayer Perceptron (MLP), and traditional physics-based models like the Gipps model. Notably, the KDNN model better prevents collisions, measured by minimum Time-to-Collision (TTC), and operates with lower computational power, making it ideal for AVs or driving simulators requiring efficient computing.