In this paper, we investigate an underlay cognitive non-orthogonal multiple access (NOMA)-based coordinated direct and relay transmission network with imperfect successive interference cancellation, imperfect channel state information, and co-channel interference caused by a multi-antenna primary transmitter. In the secondary network, a source communicates with a near user via direct link and with a far user through the assistance of multiple relays subject to transmit power constraints. Four relay selection schemes are proposed to enhance the performance of NOMA users and the overall system throughput. In our analysis, exact closed-form expressions for the outage probability (OP) of NOMA users and for the overall system throughput are derived. To provide further insights, a performance floor analysis is carried out considering two power-setting scenarios: (i) the transmit powers at the secondary source and relays go to infinity and (ii) the peak interference constraint goes to infinity. Towards real-time configurations, we also design a deep learning (DL) framework for the OP and system throughput prediction. Our results show that the deep neural network exhibits the lowest run-time prediction and root-mean-square error among the proposed DL models. Furthermore, the predicted results based on DL framework match with those of the analysis and simulation.