Translation:Now they don't even have a bottle of water.
Yes, for your first question. In negative sentences you use "non... neanche" or "non... nemmeno" or "né... né".
In English, you use "neither... nor" for two or more things in the negative, e.g.: "They do not have neither wine nor beer", in Italian is the same: "Non hanno vino neanche/nemmeno/né birra", but "Now they do not even have water" "Ora non hanno neanche/nemmeno acqua".
In affermative sentences you use only "anche/pure"
Would anyone care to explain to me why the now HAS to be at the beginning of the sentence in English and not at the end? I speak English, and both sound completely natural to me -- it just depends on what you want to emphasize. "A year ago, they owned the city; now, they don't even have a bottle of water." "The recession took a toll on their formerly lavish lifestyle; they don't even have a bottle of water now."