exphrasis

As it was explained to me, PhDs and MAs are required to know at least one foreign language so that they may engage with critical texts and analyses published by scholars in journals that are written in a language other than English. 
One might argue that it is a bit of an "old school hold-over from the European-American academy" (not my words, haha), in that there are many ways to translate articles today that (I guess?) don't require you to actually be reading-fluent in another language. Nevertheless, it remains a requirement as it is obviously necessary that one can keep up with at least the written work in their field. And, if I'm honest, being able to read an article (armed with a dictionary and grammar chart if needed) is usually a lot better than relying on an online translation resource. 
Also - I haven't heard of it being related to what you study. Granted, the transnational turn has prompted Anglophone scholars to consider translated texts and texts that incorporate other languages (hence why having another language that ties into your work (if applicable) is a bonus), but - even if you only read things originally (and totally) written in English - you're expected to be able to at least read articles in French/German/Spanish/etc. that also deal with those Anglophone texts. 
Hope this helps!
*Source: I was focused on Anglophone texts as an MA and had a language test requirement (I had to translate a literature article pass/fail) and will be starting a PhD as an Anglophone studies person and also have a foreign language requirement (I imagine the test is similar to my MA language test.)*

I can't recommend Belcher's Writing Your Journal Article in 12 Weeks. It's a fantastic resource and is fashioned more like a workbook that works you through each step of the article writing process. When I was writing and revising my first article, I found Belcher's timeline of what you should be doing each week to write/prepare the article so useful. It made the whole process seem so much more manageable. 

The letterhead is entirely unnecessary. It's used for official communications from your position in the department (e.g. writing someone a reference letter), or on behalf of the department as a whole. It can also be used to prepare cover letters for job applications. But not a whole lot more, and as a grad student the only relevant potential use is the last one.
Cover letters accompanying journal submissions run the gamut from trivial and irrelevant to a serious requirement. From what you've said, it sounds like yours is mostly just a formality used by the editors to screen the submission/find referees, and then to contact you later (which is to say, to help them identify which paper was yours; contact will almost certainly be by email). Sometimes journals want a more involved cover letter, in which case you should give a few sentences summing up your paper's argument, why it's a good fit for the journal, how it fits in with recent work published in the journal, etc.
Alternately, if you have a weird paper, the cover letter is your chance to convince the editors to give it a chance (and to help them find suitable referees by being upfront about its weird content). I have a weird paper coming out soon in a really good journal that was like that: it marries the methods and results of three disciplines to get a handle on a single problem, and opens an entirely unexplored avenue of historical research in the process. It flunked hard, over and over again, for years and years, until I realized that I could pre-empt a lot of the pushback I was getting by explaining, in my cover letter, exactly why the approach I took was necessary, being clear about its interdisciplinary nature, and telling the editors just what I thought upshot was for work in my discipline. I immediately got much better-qualified and more supportive referees, and the editors themselves seem to have had a lot more faith in the paper.
As I said, yours sounds like it doesn't need to be anything like so involved! I just thought it might be handy to say a bit more, in case you or anyone else ever needs to write a more involved cover letter.