Supported bimetallic nanoparticles (NPs) often display improved catalytic performances (activity and/or selectivity). Yet, structure-activity relationships are difficult to derive due to the multitude of possible compositions, interfaces and alloys. This is notably true for bimetallic NPs used in the selective hydrogenation of CO₂ to methanol, where the NPs respond dynamically to the chemical potential of the reactants and products. Herein, we use a combined computational and experimental approach that leverages ab initio Molecular Dynamics (AIMD) and Metadynamics (MTD) in conjunction with in situ X-ray absorption spectroscopy, chemisorption and CO-IR, to explore the dynamic structures and interactions with adsorbates under various CO₂ hydrogenation conditions in highly active and selective silica-supported PdGa NPs. We find that PdGa alloying generates isolated Pd sites at the NP surface, changing the dominant binding modes of relevant adsorbates compared to pure Pd NPs: CO molecules mainly occupy atop sites and hydrides switch from mainly internal to atop and bridge sites. Under more oxidizing conditions, akin to CO₂ hydrogenation, Ga is partially oxidized, forming a GaO_X layer on the NP surface, with a partially dealloyed PdGa core and some remaining isolated Pd surface sites. Overall, these bimetallic NPs show high structural dynamics and a variable extent of alloying depending on the adsorbates relevant to CO₂ hydrogenation. This work highlights that AIMD/MTD is a powerful approach to elucidate structural dynamics at a single particle level in complex catalytic systems.