The rapid expansion of Internet of Things (IoT) networks has led to an exponential increase in data generation, raising significant network bandwidth bottlenecks and severe data privacy concerns. Traditional centralized Artificial Intelligence (AI) models rely on transmitting raw, sensitive user data to distant cloud servers, which introduces latency overhead and elevates the risk of data interception. To address these critical challenges, this study introduces a novel decentralized edge-AI framework based on Federated Learning (FL) specifically tailored for secure, low-latency communication networks. We design a hierarchical federated learning architecture that integrates a client-side adaptive optimization algorithm (FedAvg-Adaptive) deployed across distributed edge-computing devices. This adaptive mechanism optimizes local gradient aggregation to mitigate convergence instability caused by device heterogeneity. To robustly secure local parameter transmission against potential reconstruction and eavesdropping threats, we implement a lightweight Differential Privacy (DP) mechanism using calibrated Gaussian noise addition. The framework is systematically evaluated on a large-scale real-world benchmark dataset of IoT sensor communications, simulating up to 100 heterogeneous edge nodes operating under Non-Independent and Identically Distributed (non-IID) data distributions. The experimental results demonstrate that the proposed FedAvg-Adaptive model achieves a classification accuracy of 92.4% in anomaly detection tasks while reducing communication bandwidth consumption by 43.1% compared to traditional centralized learning paradigms. Furthermore, the integration of lightweight differential privacy successfully mitigates membership inference and data reconstruction attacks without introducing substantial computational or energy overhead on resource-constrained edge hardware. Overall, this study proves the feasibility, scalability, and efficiency of privacy-preserving federated learning in next-generation information and communication technologies, providing a secure and bandwidth-efficient foundation for future smart IoT infrastructures.