Simultaneous wireless information and power transfer (SWIPT) and full-duplex (FD) communications have emerged as prominent technologies in overcoming the limited energy resources in Internet-of-Things (IoT) networks and improving their spectral efficiency (SE). The article investigates the outage and throughput performance for a decode-and-forward (DF) relay SWIPT system, which consists of one source, multiple relays, and one destination. The relay nodes in this system can harvest energy from the source’s signal and operate in FD mode. A suboptimal, low-complexity, yet efficient relay selection scheme is also proposed. Specifically, a single relay is selected to convey information from a source to a destination so that it achieves the best channel from the source to the relays. An analysis of outage probability (OP) and throughput performed on two relaying strategies, termed static power splitting-based relaying (SPSR) and optimal dynamic power splitting-based relaying (ODPSR), is presented. Notably, we considered independent and non-identically distributed (i.n.i.d.) Rayleigh fading channels, which pose new challenges in obtaining analytical expressions. In this context, we derived exact closed-form expressions of the OP and throughput of both SPSR and ODPSR schemes. We also obtained the optimal power splitting ratio of ODPSR for maximizing the achievable capacity at the destination. Finally, we present extensive numerical and simulation results to confirm our analytical findings. Both simulation and analytical results show the superiority of ODPSR over SPSR.