The names of people who lived before the Tower of Babel often have meaning in Hebrew. Like "Adam" is the Hebrew word for "human" because he was the first human. "Eve" sounds similar to the Hebrew for "to live", because, Adam said, she was the "mother of all living people". "Enoch" sounds like the Hebrew for "dedicated". Etc. Other mentions of language in pre-Babel days make sense in Hebrew, like Adam calling Eve "ishah" (woman) "because she was taken from "ish" (man). Etc. This rather implies that the pre-Babel language at least shared a lot of vocabulary with Hebrew. If, say, the pre-Babel language had been English (obviously absurd for dozens of reasons, but I'm making a point), the explanations of these names and other words would not make sense. Why would God call the man "Adam" because he was the first human? What does being human have to do with the word "Adam"? Etc. So it's plausible to suppose that the pre-Babel language resembled Hebrew.
RE the mechanism: This is highly debateable. I think the answer is a definite maybe. Whether the mechanism for a miracle is completely unique and involved a special creative act, or whether God used things already in place in the universe, could be hard to say. Perhaps with sufficiently advanced science we could identify exactly what God would have had to do to people's brains to change their languages. I don't know of anyone who's demonstrated anything in this particular area, though.