I realize the universal translator is just a hand-wave to avoid the "Aliens Speaking English" trope, but there are at least some basic rules established for it:
When it translates, it will use the closest approximation in the database, it can learn as it hears more of a new language, it's apparently a neural implant (at least with Ferengi), and probably a few more that I'm missing.
Does it keep the original speaker's voice, tone, inflection, and in this case, melody? Does Kira hear Vic singing in perfect Bajoran or is the universal translator belting out Frank Sinatra in Lwaxana's voice? Do the lyrics still make sense with the computer translation?
I very rarely complain about the UT, and I enjoy the Vic Fontaine component, but I just have a hard time combing the two lol.
Sometimes I wish they would have gone with a "standard" language like Space Esperanto that just sounds to the audience like English rather than the UT.
Update: I completely forgot Federation Standard existed, and that's probably the language Vic is using, and Kira is very likely fluent due to her time spent on DS9. It's kind of a retcon since that wasn't mentioned until DIS, but I can live with it.
The UT can also tell somehow when the speaker doesn't want their words translated. Anytime Worf says something in Klingon, or any Vulcans talk about their culture, they're able to say their words as they normally would.
It must have some kind of ability to translate meaning, not just words. That's probably why in Lower Decks it's able to translate some Tamarian now. Once they started working with the Federation, we were able to teach the UT some context for their metaphors.
The real question is, when Quark uses a human idiom, is he actually saying that, or is it a translation of a similar Ferengi phrase?
Yeah, I always wondered how explicit Klingon made it through the UT unchanged, lol.
Most characters, I'd guess it was massaged through the UT. With Quark, though, it could probably go either way. He's frequently interacting with a diverse crowd, so he probably is pretty fluent or at least capable in an array of languages. Wouldn't surprise me at all if he was using the idioms directly rather than having Ferengi phrases translated.