A common misconception is that none must always be treated as singular. The customary support for this view is that none necessarily means "not one" (implying singularity); in fact, "none" is just as likely to imply "not any" (implying plurality). As noted in The American Heritage Dictionary: "the word has been used as both a singular and a plural noun from Old English onward. The plural usage appears in the King James Bible as well as the works of John Dryden and Edmund Burke and is widespread in the works of respectable writers today."
I'm not sure I understand your question, but nenhum is used in the negative, as a translation of "none" or "not one", while qualquer is used as "any" or "just any" (if it is used at the end of a sentence). Have you seen nenhum used meaning "any"?
Perhaps it can be translated as "not any", but it would have to be a negative since the word nenhum originates from the Portuguese words "nem um", which literally means "not even one". I hope this helps. =)
That is a good question. The é refers to the word "nenhum", and not "nós". If it referred to nós, the word would be "somos".
São would actually be referreing to eles/elas. But the sentence "nenhum deles é perfeito" would still use an é, since it still refers to the word "nenhum".