Are 1 mole of water has a mass equal to 1 mole of steam or 2 mole of H and 1 mole of O

When water turns from liquid to steam, the molecules of water remain intact. So, steam is composed of H2O molecules moving about. Steam is not composed of a mixture of H and O.

The way your question is phrased, the answer is yes (and the previous poster dealt with the answer just fine), but I wanted to address the possibility that you were wondering if the water, on becoming steam, also separated into two moles of H and one mole of O atoms for every mole of H2O molecules. It does not.

Yes.
18g.

One mole is just a no. and mass of molecules will be equal if you will take some compound in same quantity in either state.

The answes will be no if you will change the compound say NaCl because the masses of one mole of water and NaCl are different.

A mole of water has the same mass regardless of the physical state.
1 mol ice = 18.0 g
1 mol water = 18.0 g
1 mol water vapor = 18.0 g

1 mol oxygen = 16.0 g
2 mol hydrogen = 2.00 g
1 mol H2O = 18.0 g