A) In character, how much time do we have? What is our genuine estimate for when Leaf/Hazou is going to get into a battle with the Akatsuki and need to kill them? Runes to help us make more Runes is great, unless we run out of time to make the Runes we actually need because we ran out of time making helpful prep Runes.
I give it a couple months at the minimum, somewhere between 6-12 at the upper end. The swan song of this gambit will be when the Akatsuki come looking for Hazou and don't find him, and don't take Naruto's excuses for an answer. Once they put their foot down and insist on meeting us, the jig is up and we only have a matter of days left to either put our plan into motion or do something else like go missing.
We should have at
least a couple months since they just visited Leaf and have no real reason to show up again so soon, but after that it's not really clear, and we won't know whether we're a week or half a year away from the deadline until the fateful message from Naruto arrives. We have to play both angles: building up longer-term research plans as if we have plenty of time ahead of us and optimizing our short-term deliverables just in case they soon wind up needed.
B) Out of character, this may be a warning from them to get moving on it because there's only so long they will be on board with lighthousing - they have warned us enough times that they'll allow lighthouses, but at the cost of other things still progressing potentially to our detriment.
Is this new Kage in Sand an example of that or just of world building generally? Hard to say, but they were without a Kage for so long that the premise that there was a ninja able to gain unanimous approval so abruptly is...suspicious.
I wouldn't take this part quite so far, though. The farthest the QMs have taken that logic is something along the lines of "when we're busy discussing a fast-paced and involved storyline, we're not discussing the other goings-on in the world, which means some events might happen later than they probably should've." They've ominously waggled their eyebrows about this because in theory it does present an incentive to do interesting things to keep the kaijus from landing, but I think that's mostly in fun. If a kaiju is
actually supposed to land, the QMs would only ever let themselves be delayed a little bit, lest the situation grow unsimulationist.
When I look at this Sand case study, I don't see anything too surprising. Chiyo, the previous Kazekage, was a very old S-Ranker who stepped up because she was the strongest ninja in the village at a time when they were desperately weak. Either she died in the war or took advantage of the new peace to retire and let a promising newcomer rise to the title instead, which is a reasonable thing for her to do around this sort of time in this sort of geopolitical position. And that the Kazekage that was chosen would be one of the few ninja who survived the Battle of the Gods is, ultimately, also of little surprise. The events and the timeframe are both very reasonable and I cannot meaningfully consider them a warning of anything other than "the QMs do indeed have the time to discuss these topics and make sure world events happen on time".
Broadly speaking, that's actually the baseline I operate from. It's fairly intuitive, after all, to just assume that events in the world happen on their own timetables, because that's how it normally works. From that angle, it could be said that getting into a complex involved storyline would artificially suppress that and make the external world less "happens on its own timetables", just a bit, until the current arc resolves and QM attention is freed up. But we haven't really been making plans around that artifical suppression, when it's just more intuitive (and, most of the time, more correct) to just expect the QMs to make relevant world events happen when they're meant to happen.
I certainly wouldn't expect the QMs to start throwing bigger and bigger events like this at us as punishment for going on the lighthousing mission until we finally go home. Time's passing, 's all, at a pretty fast rate because we came out here in order to have nothing to do but optimally spend our time.
