The large-scale adoption of hydrogen and its co-combustion in gas turbines is critical for achieving carbon neutrality goals. This study examines the ignition characteristics of pure hydrogen and hydrogen-methane blends, with methane content ranging from 0% to 70%, in a shock tube at temperatures between 950-2,100 K and pressures from 1.2 to 5.0 atm. The results show that increasing the methane content leads to longer ignition delay times, indicating a significant reduction in combustion reactivity. A combustion kinetic model for hydrogen and methane was also developed, demonstrating accurate predictions of ignition delay times across various blending ratios, pressures, and temperatures. Rate of production and sensitivity analyses reveal that, compared to pure hydrogen, the addition of methane increases CH3 radicals while decreasing H radicals. This shift causes methane-driven reactions to dominate, while hydrogen-related reactions weaken. Methane co-firing thus provides flexible control over ignition delay times, offering a direct means to adjust fuel reactivity. CO2 plays a key role in next-generation gas turbines with hydrogen-enriched blends, oxy-fuel combustion, and combined cycles involving shunt and recompression, all of which contribute to flexible fuel usage, low emissions, and high efficiency. This work also investigates the diluent gas effect of CO2 on the hydrogen-methane co-firing system. It is revealed that CO2 affects ignition delay in two key ways: it shortens delay due to its high specific heat capacity, yet it can also lengthen it by competing with H radicals.