Human Activity Recognition (HAR) using channel state information (CSI) is crucial for advancing healthcare applications, enabling non-invasive monitoring for improved patient care. However, traditional HAR techniques mainly rely on centralised data processing, which necessitates the sharing of raw data. This approach raises privacy concerns, leading to inefficient bandwidth usage and incurs significant communication overhead and latency, thereby limiting real-time performance and scalability. This paper introduces FedFusionQuant (FFQ), a novel federated learning (FL) framework that integrates advanced signal processing, feature fusion, and model compression during the training process. The proposed framework utilises the federated distance (FedDist) algorithm to adapt parameter adjustments based on neuron dissimilarity measures, effectively mitigating overfitting. Additionally, the incorporation of quantisation-aware training (QAT) allows the model to maintain high accuracy while substantially reducing model size. Extensive empirical evaluations demonstrate the efficacy of FFQ, showing a significant improvement in classification accuracy and energy efficiency through feature fusion and QAT. Furthermore, model compression with QAT achieves a 47% reduction in communication overhead while maintaining accuracy comparable to state-of-the-art methods.