This question is more about linguistics than history, but since it heavily draws from historical linguistics/philology (and /r/asklinguists is a dead sub) I thought I'd inquire about it here.

It seems, from my limited linguistic experience (English, Portuguese, Latin and notions of some other languages), that natural languages share core syntactic notions, such as in basic morphology (in classifying words as nouns, adjectives, adverbs, etc.) and in the possible ways to combine their meanings as a unit (more concretely, clause classifications seem to be the same).

Regarding European languages, this is not too surprising, given the influence Latin had due to the Roman Empire and the Church, and due to the postulated Proto-Indo-European language. However, theories such as Chomsky's Universal Grammar seem to suggest such commonality extends to all languages, well beyond those covered by these explanations.

So my question is: are these curiously reoccurring syntactic (and to some extent semantic) elements in fact universal across contemporary and ancient languages? If so (and this strays somewhat from history), are there historical, psychological or phenomenological theories or conjectures attempting to explain (instead of merely postulate) this astounding coincidence?

EDIT: clarification