And to expand on that question: Why was it acceptable to translate the Bible into these four languages, but translating it to other languages (e.g. German) was considered heresy? I assume the underlying cause is the same for both questions?

Well, several Greek and Middle Eastern churches still use Aramaic and Koine (New Testament) Greek as first-class liturgical languages. Some of those are Catholic, in that they are in full communion with the Holy See - examples of churches using Aramaic include the Maronite Church and the Chaldean Catholic Church. So that's a trite answer - those parts of the Church that started with Middle Eastern languages never stopped. But what about the Church in Rome? What happened there?

To answer that we need to look at the history of the Church in Rome. The earliest evidence can be seen in the Bible, in Paul's letter to the Romans (written around AD 60) - Paul wrote in Greek, presumably to an audience literate in that language. Around 20 years later, Pope Clement I was still writing letters in Greek to other churches - his stint in office ended in AD 99, so that covers the first century AD.

The change to Latin as the working language of the Church in Rome seems to have occurred in at the end of the second century AD, with the election of the first African Pope, Victor I. All of our surviving records of Victor's correspondence are in Latin, and we don't have any evidence that he knew Greek. This seems, as far as we know, typical of African bishops. A later example off the top of my head is Augustine of Hippo. He lived two hundred years later, knew Latin and not Greek and was not hindered by this by his time in Rome.

So, to answer: the Roman Church started with Greek as a working language, and seems to have moved to Latin as a practical measure, perhaps under the influence of a Pope who didn't know Greek. Hebrew and Aramaic were regional languages and we have no evidence of their liturgical use in Rome.

The short answer to this question is largely that, for a variety of reasons that begin with St. Peter (the first Bishop of Rome/Bishop of the Church) and St. Paul (the author of several of the texts in the New Testament and a loyal Roman subject) and end with Emperor Constantine (the Roman emperor who first legalized Christianity across the Empire and established a precedent for the position of the emperor as having great influence and ultimate regulatory authority over religious discussions and councils of that time), the Catholic Church ended up being based in Rome as a subsidiary of the Roman Empire in the post-Constantinian era. Latin was the official language and lingua franca of the Empire and thus the language of the official church of the Empire; additionally, starting with the Edict of Thessolonia in 380, Christianity became the official state religion of the Roman Empire. Again, Latin being the official language of the Empire meant that it inherently became the language of the Empire's official state religion.

Even as the use of Latin as a common, spoken language declined in the wake of the Roman Empire's collapse in the 6th century, the Church just continued to use Latin because theological texts and education had by that point become relatively standardized across the continent (later in the Medieval era, French was also utilized, but Latin was seen as the language of theology and scholarship by that point). Technically the Church could have used Greek since it was the other official language of the Roman Empire and also an incredibly common language, but Latin was the language of imperial administration, legislation, and the military for essentially the entire Imperial era and was thus higher up hierarchically on the language food chain.

A slightly more specific answer is mostly related to St. Jerome's translation of various scriptures into Latin (resulting in the Vulgate in 382 AD). The Pope who commissioned the Vulgate's creation ordered it to be used as the official Biblical text throughout the Empire, which heavily contributed to the adoption of Latin as the standard language of the Church (if the official authoritative holy text of your tradition is in Latin, it makes sense to use Latin as the standard language for all official theological purposes). Since "The Church" as an institution really didn't exist in any form we would recognize until the Council of Nicaea in 325 AD and wasn't legalized as a public institution until the 370s, the Vulgate for all intents and purposes was the first and only "complete" version of the Bible the Church endorsed for nearly a thousand years; it was the definitive version of the text. Obviously, this led to Latin as a language having an enormous influence within the Church since the only authoritative version of the text was in Latin.

Anyway, the standardization process was further codified by the translation and dissemination of several other theological texts in Latin, incredibly influential theological figures such as Augustine of Hippo and Jerome writing primarily in Latin, and ultimately, the Tridentine Mass in the 1570s, which created a standardized liturgy--in Latin--for church services (which was actually standard in all Catholic churches up until the 1970s!).

Basically: It was easiest and most efficient to use the most widely-spoken language at the time, especially for the purpose of converting pagans. Also of incredible historical significance is the fact that as the Church became established in and based out of Rome, they used Latin as it was the official language of the Roman Empire. Additionally, since the Vulgate was essentially the only officially endorsed translation of the Bible, Latin had an enormous influence within the church due to the Vulgate being written in Latin. Once the use of Latin for Church purposes became standardized, it was easiest to simply keep using it, even after people largely stopped speaking it in everyday life (also by that point Latin had become the language of theology and scholarship, so the education factor played in as well).