In this article, we study novel wireless powered cognitive nonorthogonal multiple access (NOMA)-based Internet-of-Things (IoT) relay networks to improve the performance of a cell-edge user under perfect and imperfect successive interference cancelation (SIC). In the secondary networks, a source node communicates with a cell-center user via direct link and with a cell-edge user through the assistance of a master IoT node under cognitive radio constraint. Exact closed-form analytical expressions for the outage probability (OP) of NOMA users and the overall system throughput are derived. To provide further insights, a performance floor analysis is also carried out considering two power-setting scenarios: 1) the transmit powers at the power beacon goes to infinity and 2) the maximum allowable power constraint goes to infinity. Moreover, we develop two iterative algorithms for minimizing OP users and maximizing system throughput subject to time-switching and power-allocation factors in two-hop transmission. Direct derivation of the closed-form expression for the ergodic capacity (EC) becomes unfeasible due to the high complexity of the proposed system model. To overcome this issue, we design a deep neural network (DNN) framework for the EC prediction toward real-time configurations. Our results show that the predicted results based on this DNN framework perfectly align with the simulations, validating our design framework. In addition, the DNN approach exhibits the lowest root-mean-square error and low run-time predictions among other regression models.