The Sixth-Generation (6G) network envisions pervasive artificial intelligence (AI) as a core goal, enabled by edge intelligence through on-device data utilization. To realize this vision, federated learning (FL) has emerged as a key paradigm for collaborative training across edge devices. However, the sensitivity and heterogeneity of edge data pose key challenges to FL: parameter sharing risks data reconstruction, and a unified global model struggles to adapt to diverse local distributions. In this paper, we propose a novel federated learning framework that integrates personalized differential privacy (DP) and adaptive model design. To protect training data, we leverage sample-level representations for knowledge sharing and apply a personalized DP strategy to resist reconstruction attacks. To ensure distribution-aware adaptation under privacy constraints, we develop a privacy-aware neural architecture search (NAS) algorithm that generates locally customized architectures and hyperparameters. To the best of our knowledge, this is the first personalized DP solution tailored for representation-based FL with theoretical convergence guarantees. Our scheme achieves strong privacy guarantees for training data while significantly outperforming state-of-the-art methods in model performance. Experiments on benchmark datasets such as CIFAR-10 and CIFAR-100 demonstrate that our scheme improves accuracy by 6.82\% over the federated NAS method PerFedRLNAS, while reducing model size to 1/10 and communication cost to 1/20.