Endotracheal suctioning (ES) is an invasive yet essential clinical procedure that requires a high degree of skill to minimize patient risk - particularly in home care and educational settings, where consistent supervision may be limited. Despite its critical importance, automated recognition and feedback systems for ES training remain underexplored. To address this gap, this study proposes a unified, LLM-centered framework for video-based activity recognition benchmarked against conventional machine learning and deep learning approaches, and a pilot study on feedback generation. Within this framework, the Large Language Model (LLM) serves as the central reasoning module, performing both spatiotemporal activity recognition and explainable decision analysis from video data. Furthermore, the LLM is capable of verbalizing feedback in natural language, thereby translating complex technical insights into accessible, human-understandable guidance for trainees. Experimental results demonstrate that the proposed LLM-based approach outperforms baseline models, achieving an improvement of approximately 15-20\% in both accuracy and F1 score. Beyond recognition, the framework incorporates a pilot student-support module built upon anomaly detection and explainable AI (XAI) principles, which provides automated, interpretable feedback highlighting correct actions and suggesting targeted improvements. Collectively, these contributions establish a scalable, interpretable, and data-driven foundation for advancing nursing education, enhancing training efficiency, and ultimately improving patient safety.