In this work, we consider a full-duplex (FD) relay-assisted cooperative non-orthogonal multiple access (FD-CNOMA) network and examine the physical layer secrecy (PLS) performance with multiple non-colluding eavesdroppers, considering residual self-interference (RSI) at the FD relay, residual hardware impairments (RHI) at the transceivers and imperfect successive interference cancellation conditions. Initially, we develop analytical equations for the secrecy outage probabilities (SOPs) of the downlink users and the system SOP (SSOP) of the FD-CNOMA network. It is observed that the users suffer notably higher SOPs and exhibit zero-diversity order, leading to an outage floor in the high transmit power regime. In order to enhance the PLS performance, we suggest a jamming-assisted (JA) framework and evaluate the SOPs and the SSOP through analytical and simulation studies. In comparison to the network without a jammer, the suggested JA framework greatly lowers the SSOP and the SOPs, while the diversity order is enhanced to unity, provided both RHI and RSI are negligible. We also develop a deep neural network (DNN) framework for accurate and fast prediction of SOPs and SSOP, that can overcome the limitations of the intricate mathematical modelling approach. For further improving the PLS performance, we determine optimal transmit powers for the users at the BS and at the relay that separately minimizes the SSOP of the JA-FD-CNOMA network. The findings indicate that, in comparison to equal/random power allocation approaches, the suggested approach leads to a significant reduction in SSOP and SOPs and a notable improvement in system secrecy throughput (SST) and secrecy energy efficiency (SEE).