Major Spoilers for all Expansions - Some general things I didn't understand

[Enkidoh]

What about language, does everybody in the world also speak the same language, except for some very rare cases? Do we have to assume that for the player's convenience the process of translation between different NPCs is shortened so it just appears that they understand each other?

I'd rather assume that unless stated otherwise, everybody speaks the same language.

It's been somewhat ignored for simplicity's sake here in ARR, but 1.0 explained this in better detail, that language is not universal on Hydaelyn, although the citystates of Eorzea all shared the same language, the beast tribes did not, and therefore other lands like Garlemald and the Far East would also have their own languages too (and it was actually mused by certain NPCs in 1.0 to be one of the reasons there was so much animosity between the citystates and the beastmen that was leading to Primal summonings, it was simple inability to effectively communicate between societies that was the cause of much tension, which, unspurprisingly, was being exploited behind the scenes by the Ascians). Even the moogles had their own unintelligible language - the fact that the player's character could understand easily what moogles were saying was the first indication something very strange was going on in 1.0's Gridanian storyline.

The Echo was therefore used as a convinient tool to both make use of this for dramatic tension and also neatly sidestep gameplay issues where it was easy to just have every NPC speak the same language from your perspective with a ready explanation as to why that was possible (and even that was not universal, as it was clear that not every Echo user actually had the ability of xenoglossy - there was a funny scene for instance in 1.0 where sylphs invaded the Waking Sands and not even Minfilia could understand what they were saying - she had to literally get the player's character to translate Sylphic for her).

Needless to say, ARR changed this somewhat where this whole thing was kind of brushed over with minimal explanation and everyone just speaks the same language (although the Ascians were initially depicted as speaking their own outright alien language, and this even popped up in ShB and EW from time to time with Ancients also speaking alien-like gibberish, and yet other times the Ancients could be easily understood, especially when the player goes to Elpis, so it still was rather confusing.).