How would they deal with the language problem when they met new cultures / people?
Did the Greeks and/or Romans have anything approaching a professional role for translators?
If yes, were any of them famous?
Any legendary stories or multi-lingual people the way you sometimes read now and then about some prodigal 14 year old who's fluent in 14 languages?
Any controversies where translators' translations were thought to be deliberately dishonest for ulterior motives?
Thank you for your answers.
Mithridates VI, King of the Black Sea Kingdom of Pontus was reputed to be fluent in between 22 and 25 languages, according to Pliny (Plin. Nat. 7.24) and Aulus Gellius respectively (Gel. 17.17). Both of these sources mention that it is abnormal for him to not use translators/interpretors, which answers another portion of your quesiton; that monarchs - at least hellenised ones - normally employed such people. Another royal renowned for languages was Cleopatra VII of Egypt (That Cleopatra) who was allegedly the first of the Ptolemaic line to speak Egyptian (Plut. Ant. 27.3-4). I have a felling that slave prices changed in accordance with the langauges that they were able to speak but I could not provide a source. I hope this is useful to you.
Sources: Historia Naturalis - Pliny Attic Nights - Aulus Gellius Life of Antony - Plutarch