Federated learning (FL) enables collaborative medical image analysis across decentralized institutions while preserving data privacy. However, real-world deployment faces critical challenges: modality heterogeneity, where clients possess incomplete or varying medical image modalities, and cross-disease generalization, requiring models to adapt to unseen pathologies with anatomical consistency. Existing methods like FedAvg, FedProx, IOP-FL, and PntTranForFL assume uniform modality availability and static client participation, leading to poor performance under realistic clinical constraints. We propose TADynFed, a novel framework for the Heterogeneous Federated Learning (HFL) paradigm, which addresses both data and modality heterogeneity through, a tissue-aware disentanglement strategy that decouples modality-tailored and modality-shared features, a dynamic prototype memory bank for missing modality compensation, an adaptive aggregation mechanism that accounts for client reliability and tenure. We evaluate TADynFed using multi-disease MRI datasets including BraTS21 along with cross-domain imaging data from CheXpert (chest X-ray) and Hep-2 (microscopy), simulating a 13-client FL environment. The proposed framework achieves an average mDice score of 66.03%, significantly outperforming baseline methods such as PointTransformerFL at 58.60% and FedAvg at 53.06%. It also attains the lowest boundary alignment error with an ASD of 1.85 mm and HD95 of 8.70 mm, surpassing existing approaches by notable margins. In terms of calibration stability, TADynFed records an ECE of 0.09, indicating superior confidence reliability. Furthermore, it demonstrates high communication efficiency with only 76 MB of data exchanged per round, compared to 95-105 MB in other frameworks. These results validate TADynFed's ability to maintain high segmentation accuracy, boundary precision, and calibration stability while minimizing bandwidth usage. Outperforming existing frameworks by significant margins, TADynFed demonstrates robust boundary alignment, superior calibration, and efficient communication. It also exhibits strong cross-disease transferability without retraining. By integrating structured representation decomposition, prototype-guided fusion, and client-adaptive learning, TADynFed establishes a new benchmark in realistic, heterogeneous, and mix-modal federated medical imaging systems. Code supporting this study TADynFed.