If we were the White Council of Dresdenverse, Pluto would be the Gatekeeper, and Saturn would be the Blackstaff. In context of this quest, Underworld is probably some (agglomeration or colloquial name of) hellrealms attached / connected to solar system's timespace location. That, or possibly some sort of prison realm. Maybe one for spirits of the dead who were deemed unfit for reincarnation.
There is thematic overlap between Senshi anyway, not even counting Chibi Usa's future guardians - Neptune and Mercury are both water aligned, even if Mercury is more Ice, which might count as its own separate element. Neptune also shares divination with Mars, who in turn possibly shares Prophecy with Pluto (even if canonically Pluto doesn't do prophecies, as far as I know, the fanon is pervasive enough that it might be true in this quest).
My working hypothesis is that Pluto doesn't so much "do prophecies" as "receive text messages from her future self."
Using gravity powers to fly doesn't give Makoto an "Air" or "Wind" or "Flight" domain, it just lets her, y'know, fly.
Same principle. Anything you can bend your domain to do, you can do.
Also, it seems pretty clear that mages aren't
strictly limited to narrowly elemental-themed magic. Healing isn't a core domain for Ami, but she doesn't seem to have trouble learning 'Mend' once Usagi shows her.
I don't remember much of the series, but if the storyline for the PreCure Five has run all the way to its end (including GoGo? I can't remember!

), then her becoming the future queen would be a foregone conclusion. This would be like calling Usagi Neo Queen Serenity at the end of Stars--it hasn't happened yet, but it's already guaranteed.
I'm pretty sure that the Pretty Cure Five
haven't concluded their plotline, because if they had we wouldn't still have our little sleepy guy.
On the other hand, Setsuna isn't necessarily making a
prophecy in the sense of "I am telling you information about your future that
will come true." It's not something that shapes destiny in its own right or carries weight of its own. She may well just be making a
speculative prediction which, ah, happens to be inspired by her access to information about the future.