In what languages were the Nicene Creed originally written? I'm guessing it would have been Latin, the official language of the Roman Empire, but by the end of the Council of Nicea, would versions in other languages have also been created as parallel translations?
The lingua franca of the world during the early years of Christianity was Greek. Latin was the official language of Rome and used throughout the Empire for some official business, but even Rome used Greek in the Eastern parts of the empire by way of expediency. This was much more the case at the time of Christ and the early church (almost the entire New Testament being penned in Greek as a result) but it was also the case hundreds of years later. Even in the heyday of Roman cities in Asia minor, Greek was still heavily used. If you wander through ancient ruins in Turkey (where I live and the council of Nicaea was held), even the Roman era ruins are mostly covered with Greek inscriptions. A few official correspondence things with Rome appear in Latin, and not a few multi-lingual records appear, but local affairs were mostly in Greek.
Even after the Council of Nicaea would have been held and Constantinople gained prominence as the capital of the Eastern Roman Empire and Latin was the official language of government and military, most of the people in the region still used Greek and it was more common for church affairs (whether local preaching, theological writing, or church councils) to be conducted in Greek than Latin. In fact even during the rise of Constantinople, usage of Greek in education and common usage grew and Latin decreased. It wasn't really until the East/West split much later and the rise of the Roman Catholic Church that things moved west and Latin became heavily used as a liturgical language and you start finding late Patristic era church fathers writing in Latin.
Following the fall of the Eastern Roman Empire, the Byzantine Empire took it's place and returned to using Greek for politics and government as well as local affairs.
The Council of Nicaea would have been conducted entirely in Greek, and the resulting creed drafted in Greek as well. In fact much of the theological debate of the era centered around nuances of Greek words and their former usage in Greek philosophy vs. intended Christian meanings. Our terminology for things like hypostatic union, perousia, etc. all come from Greek terms predominant in theological circles of this era. There would have been almost no need to translate the Nicaean Creed into any other languages initially, it wasn't until a lot of time passed or it was carried very far afield that other translations (including Latin) start cropping up.
Several clauses of what are popularly included in the Nicene Creed are in fact not part of the original Greek, they first appear in Latin translations some years later. There has been much debate about whether these bits added by the Roman church represent sound doctrine. See for example the Filioque controversy. Whether they do or don't accurately represent Christianity is out of the scope of this question, but there is little debate that some phrases only appear in the Latin versions that don't show up in the Greek ones circulated earlier in the east.