The reactions you've mentioned involve the combination of hydrogen with various oxides and metals. Here are the balanced equations for each reaction:
H₂ + O₂ → H₂O
This is the combustion of hydrogen to produce water.Fe₂O₃ + H₂ → 2 Fe + 3 H₂O
This is the reduction of iron(III) oxide (hematite) by hydrogen gas, producing iron and water.MnO + H₂ → Mn + H₂O
This is the reduction of manganese(II) oxide by hydrogen, resulting in manganese and water.FeO + H₂ → Fe + H₂O
This is the reduction of iron(II) oxide (wüstite) by hydrogen, yielding iron and water.
In each of these reactions, hydrogen acts as a reducing agent, converting the metal oxides to their respective metals while producing water as a byproduct.