I thought about that at first, but there's really no context to it though, so it might sound a tad too personal.
That might be a cultural thing. Perhaps teachers and students are able to establish a close friendship, especially in small towns, where everyone knows each other, and one another's residency as well. Just a thought... Or perhaps these are private students and the teacher gives them lessons at their home.
For future versions can you show the infinitive/nominative along with translation when we click on the word popup?
That may be beyond their scope (or indeed on the other hand, maybe that's exactly what they intend to do). But in the meantime, until they do, or do not, get that coded, I recommend OpenRussian.org (see here for the entire conjugation of the verb, including stress marks) for conjugations. I always keep this or Wiktionary open when I'm on Duolingo - helps a heck of a lot, and my scattered brain always wants to look up all sorts of definitions to words completely unrelated to the actual assignment at hand. Hope it helps you, too.
Any comments on ученики versus студенты? Is the former more traditional/outdated and the latter more trendy?
студенты - only university students
ученики - school boys and girls, disciples in religious context, also private students or apprentices.
Because it's wrong. :) In English, you can only say "I live [somewhere]," not "I'm living"
But I heard somewhere: We are living in yellow submarine, yellow submarine, yellow submarine...
Maybe it seemed to me
No. Your word order assumes that you oppose living to other activities. Like: here they eat, and where do they live? If you want just to ask where someone lives, you put "жить" first, and the name or noun second.
The Russian does not sound clear. It sounds like he mumbles in Russian