Short form - A mana storm is a big thunderstorm that randomly throws out illusions and direct damage spells based on its rating. Kind of like Tir Na nOg's veil, if you have access to the sourcebook.
Basically this. Mana storm are big, wild, dual-natured storms that not only act like conventional storm but also sling off spells. There are also Mana Storms with almost no physical effects at all (they still toss off the spells but they're not present visually). All of them can toss out any spell on the books and any not on the books as well, but most only have one "type" of spell they cast (so the storm would be one that casts Combat magic, for instance) but that's not a hard and fast rule, it's suggested they also change their type to keep them strange and mysterious. IIR, in Target: Awakened Lands, one mana storm turned the entire population of a town into dingos and rabbits, and the dingos promptly ate the rabbits. Then it wore off. Then people needed shrinks. Things like that are apparently common.
They can be tiny like localize rain showers or large multi-mile storm fronts. They don't follow conventional rules of meteorology either. They form when and where they "want" to, move how they "want" to and end when they "want" to (I say "want" but they, so far, don't seem to have intelligence). Most are extremely destructive in their "active" phases but some don't seem to do anything at all. With the exception of the Sydney storms (and maybe a few others) they don't usually last long (under an hour). they also attract something called a Storm Wraith which usually shows up with them and they hare people with a passion.
The Sydney storms are apparently a giant aberration. They've lasted a long time and wax and wain randomly, hence their having active and inactive cycles. My guess is they're intended to be in a random cycle between "normal" storms and Mana Storms that pop up over and over in fairly rapid succession.
In my experience, most GMs who use Mana Storms (and GMs that do seems fairly rare in the States) usually swapped them up a good bit with their effects, with conditions varying inside the storm. In one area it was raining fire and had stunbolt lightning and deeper in there were illusions and acid rain, and in another part of the storm it was freezing cold, raining and turning people into wombats, that sort of variance. Basically, whatever magical effect the GM wanted to throw at you, the storm could do without real regard to rhyme or reason so long as the effect was big and powerful.
As for who "owns' Sydney. It's not quite the same as Manhattan is owned. When Sydney basically told the rest of Australia where they could stick it a few Corps stepped in to pick up the pieces and rebuild Sydney. Over time, they've become the defacto government though there are still at least elected officials who are figureheads at best. IIR (and again, no book, all this is from memory, so grain of salt here) Ares, Wuxing, the Azzies and Renraku are in along with a few others and basically make up the governmental leadership of the city.
