"The water is deep."
Translation:Vesi on syvää.
Vesi on syvä does sound a bit weird to me because I can think vesi only as uncountable noun. Syvää is in line with how other adjectives would be used in such a situation: vesi on lämmintä/kirkasta/matalaa/...
In vesi on tyyni I understand vesi referring to the surface of the water. It's a bit erratic but for some reason it doesn't sound weird at all to me. The whole sentence sounds even a bit prosaic or poetic, as do other vesi on sentences I could quickly come to think of.
Sorry for not having a proper answer, hope this helps even just a bit.
But in this sentence
only nominative is correct.
I'm not sure why that is. Judging by the number of search results from the google searches I just did, both partitive and nominative are used for "tyyni" in a predicative expression where the subject is "vesi", but nominative is about three to four times more frequent.