I wouldn't necessarilly wait for the paint to finish curing, as it'll be harder then. I've done it both ways, and unless the fresh paint is so soft that you keep micromarring it, I'd probably fix them now (especially since you're not using a rotary).
Buffer trails are the classic example of "swirls"; actually, these are the only *truly accurate* use of "swirls", it's what the word really refers to to those of us who care.
Just another form of marring, like light scratches. Sometimes they're a pain to get out, usually a) on hard paint and b when there was heat involved with putting them *in*. But quite often they're not that hard to polish out.
I'd expect the #83, followed by something milder, will take care of them. But yeah, you might try something milder first and see if that'll do it.