Would saying "Säljer du(or ni) [thing]" be the correct way to ask a clerk if their store sells an object?
That's perfectly ok, but it might be more natural just to ask Har ni …? ('Do you have …?')
I'm not a native speaker and the english sentence seems a bit odd to me... I would have either expected "You sell a fruit" or "You sell fruits". In which case would you use the sentence above?
This sentence uses "fruit" as an uncountable noun. It's just talking about fruit in general. At least to me, "you sell fruit" sounds much more natural than "you sell fruits," even though they mean the same thing.