As a next-generation wireless technology, the in-band full-duplex (IBFD) transmission enables simultaneous transmission and reception of signals over the same frequency, thereby doubling spectral efficiency. Further, a continuous up-scaling of wireless network carrier frequencies arising from ever-increasing data traffic is driving research on integrated sensing and communications (ISAC) systems. In this context, we study the co-design of common waveforms, precoders, and filters for an IBFD multi-user (MU) multiple-input multiple-output (MIMO) communications with a distributed MIMO radar. This paper, along with companion papers (Part I and II), proposes a comprehensive MRMC framework that addresses all these challenges. In the companion papers, we developed signal processing and joint design algorithms for this distributed system. In this paper, we tackle multi-target detection, localization, and tracking. This co-design problem that includes practical MU-MIMO constraints on power and quality-of-service is highly non-convex. We propose a low-complexity procedure based on Barzilai-Borwein gradient algorithm to obtain the design parameters and mixed-integer linear program for distributed target localization. Numerical experiments demonstrate the feasibility and accuracy of multi-target sensing of the distributed FD ISAC system. Finally, we localize and track multiple targets by adapting the joint probabilistic data association and extended Kalman filter for this system.