8 cases in Sanskrit and such is impressive but Hungarian has 18 singular, 18 plural, plus 6 singular possessive cases and 6 plural, for a total of 48 (though most nouns don't have an essive-modal case for either sg or pl so the effective total is 46). No language in the world has more. :)
You shouldn't count cases separately for singular and plural.
Otherwise you might as well say that German has sixteen cases instead of four, because it also has three genders in the singular.
Also, https://www.quora.com/Which-languages-have-the-most-cases/answer/Thomas-Wier?srid=uvG6 claims that Tsez has 252 cases - even 48 is not even close to that number.
That's true about the singular/plural, but Tsez only has 252 cases if you count case combinations and dialectical cases. It doesn't have very many distinct cases in the standard tongue. If you count agglutination, Hungarian has 1176 forms for each noun (though most aren't used because their meaning is strange).
I do not, though I have heard of them. I chose this name partly because of my interest in history (particularly ancient and medieval) and I've studied Wycliffe's teachings and lament the fact that he was killed by the catholic church for them, partly because I like anonymity online, partly because I like middle English (which is what his translation of the Bible was in), and partly out of distaste for the catholic church, especially in the middle ages (no offense to catholics, I just don't like the church's teachings or dark deeds). I'm not religious, but I was raised Lutheran at first, then non-denominational Christian.
I think this question is quite misleading and gives you the wrong impression that using this without the verb ('kérek') is acceptable. The translation is gramatically correct however this is considered quite rude in a lot of formal situations, especially if you are ordering in a bar or a restaurant and the bartender is asking back because he has not understand your order. If you want to express disgust or arrogance towards the waiter then it is fine of course :)
Given a certain context this might be acceptable. If you are among friends and you're asking a cup of water then your friend might not understand it and asks back "Mit? Vizet?" Then you can say "Igen, vizet" without guilty conscience :)
Putting the word 'kérek' at the end changes everything. If you are getting better at hungarian you might be able to identify the situations where it can be omitted. But I do not think a beginner course should deal with this.
You are perfectly right. The key, as you already stated, is that the question is already suggesting water. Kalitan's question can also be correct if "Would you like to drink water?" is asked in a way that you are interested in whether I want to drink water and not soda or anything else. But if this question is asked so the one asking is interested in whether the one asked simply wants to drink some water it can be answered with just saying "Igen." (Yes.) I hope I was able to help.
Definitely no. It is "víz", with long "i" and "z" at the end. If you say/write it short, it will be closer to "visz" [he/she/it carries, takes] but still misspelled. This is one part. The other is the lack of accusative, you MUST use it. But if you were asked about a transparent clear fluid if that is pálinka or víz, and there was a guess for the latter, you can say "igen, víz". See the more answers above. ;) And pay a lot of attention to the spelling and accents, because they modify the meaning of the words. Imagine the same like in English with "morning" or "mourning", or even "beach" and "❤❤❤❤❤". ;) I wouldn't mind if you call me a 'son of a beach', but the latter wouldn't be very nice ;)