I'm not qualified to answer any of your questions, but, if you will permit me to ask one based upon them I have one. (And, I'm not trying to snark, I'm honestly wondering.)
Bonus: Do you comment differently if it's an international student or not? International students are likely going back to their home countries, so it seems less necessary that they address this.
On the face of it, that makes some sense, but whether they return to their countries and stay there, or not, does this really matter? They have a degree in hand that's been awarded by your institution--which happens to be in an English-speaking country. Doesn't that come along with some level of assurances to those who see it that they are fluent in the language--at least insofar as fluency within disciplinary norms?
There's no guarantee, after all, that they are going home. Heck, they could go to a third country. The onus, of course, would ultimately be on the employer, but I'd think the degree at least suggests some level of competency and fluency in the language of the country in which it was awarded. I guess, for example, that if I met or interviewed someone with an advanced degree from the the Sorbonne I'd expect they'd be fluent in expressing themselves in French, whether or not they had grown up in France,mand whether or not I had the expertise to double-check their fluency.
Wouldn't it be at least a bit embarrassing to the institution to award a degree to someone who then, upon publishing something--or on giving a conference talk--in the language of their degree granting institution, was deemed to be semi-illiterate in the language of their program? (Or, as a corollary, might not that person's future employer find themselves somewhat embarrassed to have hired someone they assumed, based on the degree, was fluent in that other language when they were unable to demonstrate any real fluency at all when representing the hiring entities' interests with clients relying on that fluency?)
I can't think that it does the student, the institution, or any future employers any service by letting language skills slide, no matter what language(s)/countries are involved.