Engineers know that to get hydrogen it takes more energy to recover it from a compound than the energy obtained from recombining it with oxygen. Unlike carbon-stabilized hydrogen in fossil fuels, hydrogen is not found floating around in the free state.
No, batteries act as an energy source for an electrical system. Fuel cells require the oxidation of a fuel source (hydrogen or hydrocarbons) to generate electricity.
Yes, I am familiar with the issues of extracting and storing hydrogen.