Despite its promise for large-scale energy storage, underground hydrogen storage (UHS) can be affected by hydrogen-induced bio-geochemical interactions that influence operational safety, efficiency, and storage integrity. To characterize the coupled bio-geochemical processes, this study develops a thermodynamically and kinetically coupled model for microbial population dynamics that goes beyond conventional Monod-type kinetic rate laws. It integrates the thermodynamic feasibility of growth via Gibbs free energy constraints with kinetic rate expressions, and accounts for energy allocation among microbial growth, decay and maintenance metabolism. This enables dynamic prediction of biomass evolution and mass conservation. Geochemical reactions mediated by microbial activities are then explored by involving reservoir minerals and fluids that may alter porosity, permeability, and mineral composition under site-specific conditions (temperature, pressure, salinity, and mineralogy). Our results quantify risks associated with microbial hydrogen consumption, souring, and geochemically induced property changes, providing guidance for safe, efficient, and scalable UHS systems.