How are a long and a short i pronounced differently? Is it just the amount of time spent making the sound?
as a non-Hungarian who hasn't tried speaking the little I know in a long time, I would say that "i" is the one vowel for which the sound is unchanged regardless of length (accent).
The basic difference is exactly what JFORD574 said, but it's also true that "í" is quite often shortened in speech.
so if (on its own) you just wanted to tell someone you wanted water ,would you say en akarok viz?
In the sentence "I want water", water is the direct object so it should be in the accusative case. So politeness aside, it would be "Én akarok vizet"