A novel framework is proposed to integrate communication, control and computing (3C) into the fifth-generation and beyond (5GB) wireless networks for satisfying the ultra-reliable low-latency connectivity requirements of remote-e-Health systems. Non-orthogonal multiple access (NOMA) enabled 5GB network architecture is envisioned, while the benefits of bringing to the remote-e-Health systems are demonstrated. Firstly, the application of NOMA into e-Health systems is presented. To elaborate further, a unified NOMA framework for e-Health is proposed. As a further advance, NOMA-enabled autonomous robotics (NOMA-ARs) systems and NOMA-enabled edge intelligence (NOMA-EI) towards remote-e-Health are discussed, respectively. Furthermore, a pair of case studies are provided to show the great performance enhancement with the use of NOMA technique in typical application scenarios of 5GB in remote-e-Health systems. Finally, potential research challenges and opportunities are discussed.