Also, it costs about 1 million euros per year[0], I wouldn't call that very expensive on the scale of a country like France. Even if it's absolutely useless.
In practice, zero is normally singular in French unless you want to show that there is none of a number of things ("zéro produits artificiels", "zéro émissions").
[0]https://www.liberation.fr/checknews/2017/12/14/bonjour-combi...
They don't make a rule book, but they often make blog posts in which they clarify how they want "proper french" to look like.
Anybody has the right to do that, they're mostly writers so they have an opinion on the language, but at the same time they're not linguists so they can't really be a prescriptive source. They just give their (usually reactionary) opinion.
I was just making clear that they don't make the rules. The Ministry of Education kinda does, and is often at odds with the Académie especially when it comes to the orthography reforms.