No, if H2O is separated into H2 and O, then it is not the same substance
It's hard to relate a mole to carbon or sulfur. Imagine if I walked up to you and said, "What's the relation between a dozen and donuts?"
A mole is a form of measurement for atoms, more specifically, 6.02 * 10^23 atoms. I suppose you could relate it to Carbon or Sulfur, since the number of atoms of each are usually measured in moles.
Carbon and Sulfur don't have a set number of moles (Just like donuts don't have to be a dozen), so it's hard to answer your second question.
In the atomic table, the number you see under the element is the molar mass, which is the weight of an a mole of the element. In this way, I guess there's a mole of Carbon and Sulfur present, if we're looking at the periodic table.
-T.B.
