It builds on the adaptations of the last generation of speakers and is refined. Language is flexible, which is why there would be no point in programming in a full vocabulary since the child might not be able to talk with it's mother and community. The start of meaningful communication involves more than the present cues of the environment the use of symbols. This is the beginnings of grammar. Grammar and syntax arise to make sense of the strings of arbitrary symbols.
Processing becomes quicker and more efficient.
It is a fundamental feature of humanity. UG could have evolved in to the complex thing it is because of the ingeniousness of language users to create new forms and eradicate old ones within even tens of generations. To explain UG as an evolutionary adaptation is not difficult. The eye evolved from a patch, generating a lens and so on. Sorry this is so long, but I did not think there was too much of a problem with evolutionary theory.