I tried to read up a couple of wiki pages where this conflict comes from and I'm left with a couple of questions:
This article describes the conflict, from a somewhat unconventional perspective. But it does answer your questions, somewhat.
[*]has Ossetia always been divided into a northern part belonging to Russia and a southern part belonging to Georgia? Or is this a creation stemming from the 1920-1922 civil war?
The Ossetians are the remnants of the Alanii, who were chased into the mountains by the Mongols. "From then on it was just a matter of who was going to dominate them, the Russians or the Georgians. Most Ossetians preferred the Russians, who were farther away and not so damn interested in them."
As far as I can tell Ossetia has known periods of Georgian domination, Russian domination, or as divided between them. And it all stretches back a very long time.
[*]do the South Ossetians want independence as South Ossetia, have independence in a united Ossetia, or be part of Russia?
"In 1989 [...] South Ossetia declared itself united with North Ossetia. [...] Backed by the Russians and plenty of North Ossetian first cousins, the South Ossetian irregulars wound up flattening the Georgians and have been free-ish ever since."
I think they want a united Ossetia, within the sphere of inluence/under the protection of Russia.
[*]how come most South Ossetians now have Russian passports?
Ossetia is probably too small for independence in a region as, uhm,
dynamic as the Caucasus. So since they hate Georgia more it makes sense to crawl under Russia's wing, and with plenty of family members in Russian-owned North Ossetia it should be fairly easy to obtain Russian passports.
[*]how come the enmity between South Ossetians and Georgians?
"The Caucasus is a crazy maze of mountain valleys, every damn one marked off as the property of one tribe or another. Step across some imaginary line and you're walking into a blood feud that's been going since the last Ice Age. This is feudin' country that makes Appalachia look like Haight-Ashbury.
While the Soviets were in charge, the Caucasians put their feudin' gear in storage. Stalin was one babysitter you didn't act up with.
[...]
Georgia's small enough already, but even so, there are at least three parts of it that may or may not be ethnically distinct, depending on who you ask and who's got the gun at the moment.
[...]
Ossetians don't think of themselves as ethnic Georgians. The Ossetians have what you call "a glorious past," and in their case it's true."