Can't answer all of your questions, but I'll give at least a few of them a go:

• In the specific case of Sazed, it should be noted that Preservation and Ruin don't perfectly cancel each other out. In the second era, it's made comment that Harmony has trouble acting as time has gone on as the two oppose each other, but several characters talk about Saze becoming more like Ruin over time. I think this is probably because Preservation gave up part of their power into humanity and so is just generally weaker than Ruin (same reason Preservation lost influence in the world over time)
• I don't think it's nearly as clean as 8 vs 8. To date we've only really seen 3-4 "negative" shards: Odium, Autonomy, maybe Ambition, and maybe Dominion. For example, one of the shards is Whimsy, and there isn't one like "Seriousness" or anything like that
• Presumably if someone held all 16 shards, they would be like Adonalsium. Dawnshards are less clear. After the Shattering, its said the Dawnshards changed form somewhat, so who knows what holding them all would do
• I don't think shards have that level of control over their respective magic systems. At most, I think they can just restrict access to using it
• The 10 surges are associated with Honor, Cultivation, and Odium. I would say that most often, they're all associated with Honor as the vast majority of surgebinders use stormlight to access them. Lift I think is the only character in the books that uses lifelight, and that required direct intervention from Cultivation. Navani only is able to use towerlight due to her bond with the Sibling. The fused access the surges through voidlight, but even then they can only use 9 of the surges as Adhesion is more intricately related to Honor than either of the other two. I don't think they technically constitute different magic systems, but to my mind the surges are more fundamental to the foundation of magic usage within the entire Cosmere as surgebinders are essentially just slinging around raw investiture (in the form of the lights) and only gain access to them by the Nahel Bond with splinters. Presumably if there was a "higher" version of the spirits on Komashi, they may be able to form a Nahel Bond (the spirits from rock stacking highly resemble creationspren)
• Brandon Sanderson has actually talked about how it's a mistake in his books that Atium can't be burned by non-allomancers. Atium can only be used by Mistborn and Seers (atium mistings). Brandon's mistake actually makes it more confusing, but assuming that it's corrected and non-allomancers can use Atium, it makes sense because God Metals, unlike the other metals, are the actual source of investiture being the condensed investiture of the various shards. Lerasium, Atium, Trellium, and Ettmetal aren't considered part of the 16 metals because of this. So theoretically, anyone could swallow a chunk and access that investiture. Similarly, that's why anyone can use unkeyed nicrosil, it's storing raw investiture, so you would be bypassing the "through Preservation" bit. And anyone means anyone, I'm pretty sure at one point Hoid takes some Lerasium to gain access to allomancy
• At least so far that's the gist of the Cosmere arc, but honestly at this point it's too close to call. There's going to be at least 6 more Stormlight books, one or two more eras of Mistborn, sequels to Elantris and Warbreaker, a Threnody series, the fabled Dragonsteel series, and who knows what else given that he's only just started to flesh out other parts of the universe like dawnshards and aethers. He's brought on at least one other author (Dan Wells) to write Cosmere novels too. Even after 7 Mistborns, Elantris, Warbreaker, White Sand, Tress, Yumi, 4 Stormlights, and all the novellas/short stories, something tells me we're only in the beginning stages of the full ark

Hopefully this answered some of your questions.

Do the 16 shards divide neatly into eight pairs of opposing shards?

No