In the context of the Internet of Things (IoT), Tiny Machine Learning (TinyML) and Big Data, enhanced by Edge Artificial Intelligence, are essential for effectively managing the extensive data produced by numerous connected devices. Our study introduces a set of TinyML algorithms designed and developed to improve Big Data management in large-scale IoT systems. These algorithms, named TinyCleanEDF, EdgeClusterML, CompressEdgeML, CacheEdgeML, and TinyHybridSenseQ, operate together to enhance data processing, storage, and quality control in IoT networks, utilizing the capabilities of Edge AI. In particular, TinyCleanEDF applies federated learning for Edge-based data cleaning and anomaly detection. EdgeClusterML combines reinforcement learning with self-organizing maps for effective data clustering. CompressEdgeML uses neural networks for adaptive data compression. CacheEdgeML employs predictive analytics for smart data caching, and TinyHybridSenseQ concentrates on data quality evaluation and hybrid storage strategies. Our experimental evaluation of the proposed techniques includes executing all the algorithms in various numbers of Raspberry Pi devices ranging from one to ten. The experimental results are promising as we outperform similar methods across various evaluation metrics. Ultimately, we anticipate that the proposed algorithms offer a comprehensive and efficient approach to managing the complexities of IoT, Big Data, and Edge AI.