"I do not want any water."
Translation:Én nem kérek vizet.
It's correct, but it's not very polite. Children say it, or someone in the middle of the temper tantrum. 'Akar' in hungarian is ruder than 'want' in english.
You should say 'nem kérek vizet' or 'nem szeretnék vizet'.
It should be ok, also there's a little difference.
Nem kívánok vizet - implies that I'm not in the mood or not healthy enough.
Nem kérek vizet - I simply do not want it.
kér - you ask for something. It's the polite way to express what you want.
Because we often use "any" or "some" as a kind of indefinite article for uncountable or plural nouns in English -- the uncountable/plural equivalent of "a".
I am reading a book. I am reading some books. I am not reading a book. I am not reading any books.
I am eating some food. I am not eating any food.