what is the difference between voda/vodu? and kava/kavu?
One is nominative, the other is accusative. Czech nouns use grammatical cases, check the lecture notes.
This says almost the same as "Matěj má velká žizeň", doesn't it?
Firstly, velkou žízeň. Secondly, no-one said what does he need it for.
Oh, so need doesn't stand for a need to consume only
Here we have just "Matěj needs water.". It could be for anything. Washing something, extinguishing a fire, diluting something etc.