içmek istiyor is "want to drink". Your sentence is different. In "do you want water to drink", "water" is the object of the verb "want" and "to drink" is describing the water, that is, "water to drink" as opposed to, say, "water to clean with". In "do you want to drink water", "to drink" is the object of "want". you are saying that you want to drink, and then "water" is the object of "to drink".
I don't know how you'd translate "do you want water to drink", but I suspect you'd use some form of içmek placed before su.
I am still puzzled as to why "some water" is not an accepted English translation here. Also in "Ekmek yemek istiyorum." Why not "I want to eat some bread"? How would the Turkish be different to add the word "some"? And is it an important distinction? To me the two English forms have basically the same meaning.
They have distinct meanings in English too. For instance "Do you drink beer?" is asking about someone's tendencies in general. "Will you drink some beer?" is asking about whether someone would like a specific quantity of beer (a glass let's say) at a specific moment (now). Incidentally, "do you drink some beer?" would not be correct English.
"Su içmek istiyor musun?" Translation: Do you want to drink water?
Is this conman to ask this question? is (su istiyorsun mu?) the same??
This is more accurate to what you are asking: (su istiyorsun mu?) - Su istiyor musun? - Would you like some water? - (polite) unless he's a conman.
Su istiyorsun? - Do you want water?
You used "conman" & not "common."
I suppose a conman would pass off tap-water as bottled spring water. Turks don't do that.