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Tele-rehabilitation has garnered significant interest among clinicians and researchers with its potential to transform cardiac rehabilitation, affecting millions of patients annually. A critical requirement of tele-cardiac rehabilitation is a fail-safe, highly interactive system with timely feedback to both the patient and the therapists or physicians. Current systems often assume ideal network conditions, neglecting the nuances of real-world deployment. We have designed, developed, and tested an end-to-end tele-cardiac rehabilitation system that seamlessly combines Internet of Medical Things (IoMT) devices and AI-powered abnormality and activity detection, providing a fail-safe and real-time actionable closed-feedback loop system for the patient and the doctor. A pilot study evaluates system performance across diverse mobile networks in varying conditions (stable or unstable). The RESNET-18 model for cardiac abnormality detection (0.71 F1-score) and the VGG-16 model for human activity classification (0.89 F1-score) demonstrate significant performance. Furthermore, we optimize these models for edge devices, demonstrating significant speed improvements compared to cloud servers (up to 33 times faster).