[catlifeonmars]

> One theory has been that language runs on a bit of brain hypertrophied as a sort of peacock's tail

> Others have suggested language originated between mothers and children, growing out of lullabies.

Sources?

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Separately, is language unique to humans? Are there examples of convergent evolution (semblances of grammatical structure) that can give us more clues as to how language may have evolved in humans?

[ncmncm]

Grammatical language, e.g. with subclauses, does appear from evidence thus far to be unique to humans, although whalesong is complex enough that it might yet be found there.

I gather that, since the "universal grammatical structure" was promoted, languages have been discovered that are said to lack any such forms. "Said to", because very few people are reporting on them.

Sorry, for sources I would be doing the same DDGing you will.