In Australia it is always 'passerby'.

The whole sentence is actually
(The fasters arrive, one by one, or in pairs, sitting down in gloomy silence, still suffering their thirst more than their hunger.) Then, the call to prayer resounds, and the relief is written on the faces of people in the smiles they beam at you, the passerby.
Thanks for corrections.
Others may nitpick the style or word choices, but the only really important correction is "...still suffering from their thirst..."
Less significantly, I'd get rid of "of people" because we know that faces and smiles belong to people.
Still less significantly, most of your commas should go: The fasters arrive one by one or in pairs, sitting down in gloomy silence still suffering from their thirst more than their hunger. Then the call to prayer sounds, and the relief is written on their faces in the smiles they beam at you, the passerby.
Surely you want the plural
In the specific appositive construction she's written ("at you, the...") I'd actually favor the singular since the "you" is really an indirect way to give the author's perspective, not a plural "you" necessarily meant to include the readers or others in the scene.
(Vinny thinks she should lose the appositive, but I'm completely fine with it.)

Others may nitpick the style or word choices, but the only really important correction is "...still suffering from their thirst..."
I disagree, I think you could write:
"The fasters arrive one by one or in pairs, sitting in gloomy silence, still suffering their thirst more than hunger."
Down (as in sitting down) from and the second their are all obsolete.
I disagree, I think you could write:
"The fasters arrive one by one or in pairs, sitting in gloomy silence, still suffering their thirst more than hunger."
Well, you're simply wrong. When "to suffer" is followed by causes, rather than a single effect (e.g. to suffer martyrdom ) a preposition is called for, especially when two different causes are being contrasted (i.e. "thirst more than hunger.") If the OP had mentioned only "thirst" by itself, it would then be possible to treat it as an effect and omit the preposition.
Down (as in sitting down) from and the second their are all obsolete.
This is a misuse of the word obsolete+. You meant "unnecessary" or "redundant." And, again, you're wrong, at least about the "sitting down." The OP's intent is clearly that the people are arriving and doing the action of taking a seat, not that they are already seated. Ergo, "sitting down" is perfectly appropriate. (The second +their+ could be omitted with no loss of meaning...as could the first +their , for that matter.)

A better rewrite would be:
The fasters arrive. Waiting in gloomy silence, still suffering from thirst more than hunger. Then, the call to prayer resounds, the relief written in the smiles they beam at you, the passerby.
A better rewrite would be: The fasters arrive. Waiting in gloomy silence, still suffering from thirst more than hunger. Then, the call to prayer resounds, the relief written in the smiles they beam at you, the passerby.
I'm afraid not.
Besides substantially changing what the OP wrote, you've created two sentence fragments lacking subjects--a basic sort of grammatical mistake that any English teacher would give a failing mark.
