In this article, we study wireless-powered cognitive nonorthogonal multiple access (NOMA) Internet of Things (IoT) networks with short-packet communications to improve spectrum utilization and sustainability, as well as reduce the latency under imperfect channel state information (CSI) and successive interference cancelation (SIC). For performance evaluation, closed-form expressions for the block error rate (BLER) of the NOMA users, goodput, energy efficiency, latency, and reliability are derived. To gain some further insights into the system design, two scenarios can be taken into account for the positions of the primary receivers: 1) they are located near the secondary network and 2) they are located far away from the secondary network. Moreover, we propose an effective algorithm to minimize the BLERs of the NOMA users by optimizing power allocation coefficients. In addition, a novel multi-output deep-learning (DL) framework is designed to simultaneously predict the BLERs and goodputs of users towards real-time configurations for IoT systems. Numerical results show the outstanding performance of the proposed system over the orthogonal multiple access (OMA) one in terms of the BLER and goodput. Moreover, the proposed system achieves a lower latency and higher reliability compared to the long packet communications under the same channel settings. Furthermore, our designed multioutput DL also exhibits the lowest error performance and a short run-time prediction compared to the other multioutput regression models, while the predicted results using the DL model are almost matched with the simulation ones.