The electric double layer (EDL) at electrochemical interfaces plays a crucial role in controlling catalytic reactions, particularly CO2 reduction. However, a molecular-level understanding of how electrolyte composition shapes EDL structure remains limited. In this work, we develop a computational framework to explore how specific ions modulate the electrolyte microenvironment at Cu(111)/water interfaces. We develop machine learning interatomic potentials (MLIPs) using both invariant and equivariant graph neural network architectures to systematically investigate the influence of alkali halide electrolytes (LiCl, NaCl, KCl, CsCl) across a range of concentrations. We quantify specific ion effects on EDL structure by analyzing ion density profiles, hydrogen bonding networks, interfacial dipole orientations, and local electric fields. Our results reveal clear correlations between cation hydration structures and their influence on interfacial organization, as well as distinct dynamical heterogeneity and relaxation timescales within the EDL. This work provides fundamental insights into the molecular origins of electrolyte behavior at charged interfaces and establishes design principles for tailoring the EDL structure through electrolyte composition to enhance electrochemical performance.