Learn Portuguese (Portugal): Moro no rés-do-chão.

Yes, you can! Both viver and morar mean "to live." However, morar specifically means "to reside" in a physical building or address. Viver is a bit broader and can also mean "to be alive," but Portuguese speakers use them almost interchangeably when talking about their homes.

Why does the sentence use no for "on the"?

The word no is a contraction of the preposition em (in/on/at) and the masculine "the" (o). In English, we say we live "on" a floor, but Portuguese uses em for physical locations regardless of whether it translates to "in" or "on." Since rés-do-chão is a masculine noun, em + o becomes no.

What do the individual parts of rés-do-chão literally mean?

It literally translates to "level with the ground." The word rés means "flush" or "even with," do means "of the" (a contraction of de + o), and chão means "ground" or "floor".

If I go up one set of stairs from the rés-do-chão, what floor am I on?

You would be on the primeiro andar (first floor). Like most of Europe, Portugal calls the street level the ground floor (rés-do-chão or floor 0), so the very first floor you walk up to is considered floor 1.