Does за деньги only mean "for money", or is it used in the same way that we say that we do a particular job "for a living"?
Or alternatively, it would seem more natural to say "We get paid to translate articles." This isn't a literal translation either, so I'm curious as well.
I believe there are various ways to translate them. I personally would go with "Мы зарабатываем тем, что переводим статьи" or "Мы зарабатываем переводом статей" for "We translate articles for a living", and "Нам платят за перевод статей" for "We get paid to translate articles".
What's the difference between за and для, since they both mean "for"? Is there a nuance, like почему and зачем?
Usually для means "to the benefit of" and за has the meaning of for in cases like "thanks for", "responsible for", "pay for", etc. Note also that зачем comes from за and чем = for what.
Didn't I just see "за деньги" mean "about money"? I thought it was "за"... how would I say "We translate articles about money"?
I seriously doubt you could've seen it in this course. Some people do use "за" meaning "about" but it's very colloquial. AFAIK, it's a Bulgarian infuence that creeped into some southern Russian dialects, but don't quote me on that.
"We translate articles about money" would be "Мы переводим статьи о деньгах".