If Elvish is the new Common, I wouldn't count it as part of the backgrounds, just grant it. Unless slaver Elves in general don't speak Common.
Yes. Common and the other languages still exist Elves just don't make the effort to learn them, with a few exceptions.
I'm assuming that the PCs are playing non-elves?
The worker tag encompasses about everything. You can break this up a bit. Backgrounds such as cook or scribe has different skills and such. You can also expand pet to include house pet and gladiator pet.
They've expressed interest in playing this as Non-Elves so I'm at least getting started on this, but I am giving them the option of either playing the Elf or Non-Elf side of the campaign. If they choose to play Elves the existing backgrounds and class load outs work fine; might search for or make a slaver background, but other than that everything's fine.
If they choose non-elves things change. They basically get no starting equipment, no money (not that there are going to be many places they can spend it), the world is going to be a lot harder to navigate through, etc.
As for splitting up the Backgrounds I might but for right now I'm trying to keep them broad since I'm struggling with balancing 3 and haven't even started trying to write the Personality Traits, Ideals, Bonds, and Flaws.
Generally background features don't grant direct mechanical benefits like advantage on specific checks.
Yes, they are supposed to give story benefits, not mechanical ones.
Fair point, however given these characters would have no rights, freedoms, or autonomy within society I was having a hard time working out a way to give them appropriate story benefits. I am however open to suggestions if you or anyone else have some.