"No, no llueve."

the noun is 'lluvia' and llueve is a verbal form of 'llover,' to rain. Many 'weather expressions' are unusual in one way or another

no llueve = "Not raining".

no llovió = "Didn't rain"

On tip is to think about the lesson you are in to help you understand options. This is a lesson on the present tense and "didn't rain" is past tense.

In Spanish it's common to use the present verb tense where in English we would use the present participle. Here is an article on Spanish gerunds: http://spanish.about.com/od/verbtenses/a/pres_participle.htm . From the article: "The progressive tenses are used less in Spanish than they are in English."

For whatever my opinion as a Spanish student is worth, I think "está lloviendo" would work just as well as "llueve" in this sentence, but in translating from Spanish to English, "It does not rain" does not sound as natural as "It is not raining."

You changed the parts of speech. You used "rain" the noun in English instead of the appropriate conjugation of the verb "to rain".

For the purposes of Duo exercises you must translate quite closely and respect the parts of speech that express each concept.

That said, in conversational English, you can sit in a coffee shop with friends, look out the window and say "no, no rain" and they will understand that you mean "no, no it is not raining".

Idiomatic expressions are usually exempt from the requirement to translate literally because they cannot be translated word for word.

Also weird. I usually hear llueve without too much difficulty. Today, it sounded like "jueve?" and I was trying to figure out who wasn't judging, or playing...? It's a computer, you think it would sound the same all the time, but... not so much?