Deploying deep collaborative machine learning across distributed Internet of Things (IoT) edge networks requires rigorous safeguards against adversarial gradient inversion attacks and private data leakage. This paper presents a novel privacy-preserving federated learning framework integrating adaptive clipping differential privacy with lattice-based post-quantum homomorphic encryption. The proposed architecture employs dynamic noise allocation based on local client gradient variance, significantly reducing accuracy loss while guaranteeing strict epsilon-differential privacy bounds. To address computation and communication bottlenecks inherent in encrypted model aggregation, we formulate a lightweight ciphertext packing scheme that compresses encrypted gradient payloads by forty-one percent. Extensive empirical simulations conducted across heterogeneous edge testbeds utilizing standard benchmarks (CIFAR-100 and Non-IID ImageNet partitions) demonstrate that the proposed method achieves 94.2% classification accuracy while withstanding state-of-the-art model poisoning and membership inference attacks. The framework provides robust cryptographic integrity and high communication efficiency, establishing a practical paradigm for enterprise edge computing and privacy-critical decentralized AI applications. Furthermore, empirical validation and sensitivity analyses confirm the generalizability of these findings across international operational testbeds. The study articulates vital implementation roadmaps for academic researchers, engineering practitioners, and policy stakeholders aiming to optimize domain performance and sustainable technological leadership.