Naskra should confirm that the Greeks indeed used "barbaros" well before the Romans adapted the term.
Also, words change significance - Greeks may well have thought all foreigners barbarians, considering they were head and shoulders above their close neighbours (and that's an understatement), but the Romans would have had a hard time considering, say, the Egyptians less advanced than they were.
Yes they did .
Anyway , for all your etymology questions of English words that may come from Latin or Greek words (or what are the Latin or Greek words that correspond to English words , like a translation), use this website.
http://www.wordinfo.info/
barbarian, barbaryn (older spelling)
1. Etymologically, a foreigner, one whose language and customs differ from the speaker's.
2. Historically: one who is not a Greek; then one living outside the pale of the Roman empire and its civilization, applied especially to the northern nations that overthrew them; followed by one who existed outside the realm of Christian civilization.
3. A rude, wild, uncivilized person.
4. An uncultured person, or one who has no sympathy with literary culture.
5. Applied by nations, generally depreciatively, to foreigners; thus at various times and with various speakers or writers: non-Hellenic, non-Roman (most usual), non-Christian.
From Greek βάρβαρος barbaros, "non-Greek, foreign, barbarous," from an Indo-European imitative base barb, "to stammer, stutter; and unintelligible." The Greeks were quoted as saying that foreigners sounded as if they were saying, "Barbar, Barbar," which was, for the Greeks, unintelligible.