In this article, we investigate the impact of dependent channel coefficients on two-user Multiple-Access Relay Channels (MARC) with Non-Orthogonal Multiple Access (NOMA) in the presence and absence of eavesdroppers. We derive closed-form expressions for the Ergodic Sum Rate (ESR), Outage Probability (OP), and Strictly Positive Secrecy Capacity (SPSC). Using the copula method to obtain the joint probability distribution of dependent channel coefficients, our results show that negative correlation enhances ESR at low Signal-to-Noise Ratio (SNR) levels, while positive correlation significantly improves ESR at high SNR levels due to better signal alignment. The OP analysis shows that negative correlation leads to lower outage probability. Finally, SPSC results indicate that positive dependency improves performance by aligning the capacities of both users. Additionally, we derived optimal power allocation factors for each SNR and dependency condition, showing that negative dependency does not show a stable behavior in power allocation factors and occurs under unstable channel conditions. This information helps in developing better strategies for NOMA systems in urban environments. We validate our numerical analysis through simulations, confirming the trends and effectiveness of the proposed schemes in optimizing channel conditions and SNR at the base station.