Well, I hope it's not a "threat".
Join the club, very little is known for sure on the subject. Well, maybe I should say instead that there is much to learn, though certainly much is known about certain facets of syntax, semantics, and in particular phonology. The study of phonology always struck me as a window on the human mind. Syntax and semantics certainly would be much more so, if we just knew more.
Generally, the term "natural language" is used to mean what humans do, speech. It is a form certainly, of communication. ASL (sign language of the deaf) is based loosely on the language of the culture, but not really limited syntactically by the rules of English, in the case of ASL. I'm not sure one can use sign language as an argument for much of anything, except that as in the Nicaraguan case, kids can do this on their own. Something is probably hard wired in the brain to come up with a sign language, in the event they don't have a spoken language. I spent 4 years on a deaf language project which attempted to describe the syntax of the written language of the students who used ASL. It was interesting, but I'm not sure how much one can really push any of it to make claims about spoken language.
All human languages have certain universal features that seem to be just part of human psychology. Limits on the types of rules that can be used, that is. Some of it gets pretty arcane, but one example of a syntactic universal, apparently, in the transformational grammar framework, is the following:
One can say "John ate bananas and pears".
The question could be: What did John eat?
But not: *What did John eat bananas and?
To the generative grammarian, the reason that the starred sentence is ill formed, is because one element of a conjoined structure has been moved in order to form a question. While both can be moved, as in "What did John eat?", the single element cannot. This seems to be true in all languages which use movement of questioned items. Note though, that "John ate bananas and what"? is fine, since "what" is not moved.
As I say, pretty arcane, but this is how linguists look at language, or at least they used to.