Intelligent Reflective Surfaces (IRSs) are recognized as fundamental technology in the context of the forthcoming sixth-generation (6G) communication systems. Non-Orthogonal Multiple Access (NOMA) can augment fifth-generation (5G) wireless networks’ spectral efficiency. This manuscript investigates a NOMA-based downlink configuration that integrates IRS and functions in a physical layer security (PLS) scenario, accounting for self-interference (SI) inherent to full-duplex (FD) operation. The examination also considers the utilization of Fountain Codes (FCs) when faced with a potential eavesdropper exhibiting malicious intentions. This paper is evident in the development of accurate mathematical expressions for the outage probability (OP), throughput, energy efficiency (EE), and intercept probability (IP). Moreover, a Deep Neural Network (DNN) model is formulated to assess OP and IP. Subsequent Monte Carlo simulations were conducted to validate the theoretical results. More research is done on the relationship between base station (BS)-IRS-Users when the Nakagami-m fading scenario is present. The outcomes of the simulations offer the following insights: 1) Their primary aim is to corroborate the analytical expressions. 2) This investigation substantially enhances our understanding of IRS-NOMA systems, setting a foundation for prospective explorations into practical realizations. The optimal performance of the OP is presented. Furthermore, we have extended the analysis by examining the performance of two additional scenarios: one IRS without a relay and a two-IRS setup without a relay. 3) Furthermore, the results demonstrate the superior performance of IRS-NOMA compared to the traditional IRS-Orthogonal Multiple Access (OMA) approach.