Is it possible that we supply mixture of hydrogen and oxygen or hydrogen, oxygen and water to hydrogen side of fuel cell so that it can use hydrogen to produce electricity? Or any membrane that helps to separate hydrogen/oxygen/water mixer.
I recommend searching for the term hydrogen pumping as a separation technique. Hydrogen will be on both sides of the fuel cell used in this mode, but the cathode produces the "clean" hydrogen. It should in my personal opinion also with a H2/O2 mixture.
Using of a hydrogen electrode for the separation of H2 from HOН — is in principle possible, but I do not recommend doing it to you!!! The mixture of НOН gases is highly explosive (the fuel and oxidizer are in perfect proportion) and cannot be stored and even less transported to the place of use. To remove atmospheric air from the electrochemical generator, to prevent explosive concentrations, use purging with argon or nitrogen (inert gas).