Rare-disease diagnosis remains one of the most pressing challenges in digital health, hindered by extreme data scarcity, privacy concerns, and the limited resources of edge devices. This paper proposes the Adaptive Federated Few-Shot Rare-Disease Diagnosis (AFFR) framework, which integrates three pillars: (i) few-shot federated optimization with meta-learning to generalize from limited patient samples, (ii) energy-aware client scheduling to mitigate device dropouts and ensure balanced participation, and (iii) secure aggregation with calibrated differential privacy to safeguard sensitive model updates. Unlike prior work that addresses these aspects in isolation, AFFR unifies them into a modular pipeline deployable on real-world clinical networks. Experimental evaluation on simulated rare-disease detection datasets demonstrates up to 10% improvement in accuracy compared with baseline FL, while reducing client dropouts by over 50% without degrading convergence. Furthermore, privacy-utility trade-offs remain within clinically acceptable bounds. These findings highlight AFFR as a practical pathway for equitable and trustworthy federated diagnosis of rare conditions.