This paper investigates a cooperative Internet of Things (IoT) non-orthogonal multiple access (NOMA) network comprising of a multi-antenna base station (BS), a near IoT user (NU) with full-duplex capabilities, and multiple far IoT users (FU). The NU utilizes the power-splitting (PS) energy harvesting (EH) protocol and augments the harvested energy with a little energy from its battery to assist the FU. Considering the novel cooperative NOMA/non-cooperative (C-NM/NC) switching, the impact of successive interference cancellation (SIC), channel state information (CSI) errors, and nonlinear EH, closed-form expressions are derived for average blocklength error rates (BLER) of both users in finite blocklength regime. Utilizing the derived BLER expressions, the Goodput, Reliability, Latency, and battery power efficiency are expressed in closed form. We then demonstrate that the CSI errors severely degrades the performance of both the users. Monte Carlo simulations validate the accuracy of the derived analytical expressions. We also establish that a significantly better maximum performance is attained at the FU, given a target NU Goodput by the careful choice of NOMA and EH parameters. C-NM/NC switching offers a higher EE and better self-interference immunity. Results indicate that the choice of blocklength is crucial for efficient system performance.