A Hydrogen atom is one proton, one electron. The ion has lost the 1 electron, but it is still the same element, if that's what you mean. Protons are used to define what the element is.
Yes, those are both ways of describing water. The reason for the difference, is that to an inorganic chemist, the water molecule is the combination of hydrogen and oxygen, hence hydrogen oxide,...
No, Hydrogen peroxide is a compound the chemical formula H2O2. Hydrogen and element and is shown as either H or H2. Hydrogen is a gas at room temperature while hydrogen peroxide is a liquid, and is...
Hydrogen is an element on the periodic table. Hydrogen is a brinclhof element (Br, I, N, Cl, H, O, F) and as such occurs in pairs (H subscript 2) in its gaseous state.