What are the failure modes of various groups that try to keep secrets?

I think the secret should be known to as few people as possible.

If the secret requires e.g. people doing research (so with fewer people you would also have slower research), it helps if you can split the secret into smaller parts, and divide them between different people, so no one knows the entire secret; ideally they don't have an idea about what purpose their research might serve. Information is provided on a need-to-know basis, and people are punished even for leaking the little info they have. You may provide them intentionally misleading information that has no impact on their part of research.

You will probably need some kind of counter-intelligence, and maybe regularly test the loyalty of your employees by providing various controlled temptations; not only will you filter out the stupid traitors, but even the smart ones will be suspicious about actual temptations, because they will suspect it is yet another test.

At that moment you probably need to think hard about the balance of power, so you don't end up e.g. with the counter-intelligence department overthrowing the supposed leaders. Not sure how to achieve this. I think the general rule is that the inside-oriented departments (those who are supposed to handle internal bureaucracy) have more power than the outside-oriented ones (those who do the originally intended mission of the organizations). Notice how the word "secretary" originally referred to a humble assistant, but gradually "secretary general" became the most powerful role in an organization. This gets complicated.

As a dictator, how to build 100% surveillance instead of 99%, to increase the stability of your dictatorship?

I think the dictators secure their power not (only) by doing nerdy things, but mostly by being psychopaths who can credibly threaten to deliver horrible punishments even for minor infractions. When you say that any attempt to circumvent your surveillance will be punished by torturing the person, all their friends, and all their relatives to death (perhaps with the exception of the person who betrays them), suddenly everyone has an incentive to avoid doing anything suspicious and to police their neighbors and family. The dictators often stay in power by making everyone a potential enemy of everyone, and by choosing to let thousand innocent people be tortured to death rather than let one potential conspirator escape punishment.

Often as a side effect the country becomes weak at certain aspects e.g. because no one dares to deliver the bad news to the leader, and because the smart people try to leave your country, or at least avoid attracting your attention (which means they will not use their talents to the fullest).

With 99% surveillance and an LLM, a simple algorithm for a dictator is "find everyone whose behavior is unusual in any way, and have the secret police torture them until they confess". A more gentle way would be to find everyone whose behavior is unusual in any way, and force them to wear a camera on their person 24 hours a day (and kill them if they fail to do so). Also, everyone needs to give you all their passwords, and their operating system will regularly make screenshots of their activities to be archived and analyzed by the LLM (I think this is already a functionality in Windows 11).

Give huge rewards to traitors. The cheapest way for you would be to give them all the property of the people they betrayed, and maybe even make the traitors (those who survive your interrogation) their slaves. Publicly celebrate some successful traitors. The conspiracy against you may be technically possible, but most people will be to afraid to try. Also at the smallest conflict among the conspirators, some may be tempted to betray the rest (and thus gain an amnesty for themselves); and even if they are not, at least they will suspect each other, which will disrupt cooperation.

You could implant bombs in people, that can be remotely detonated, or even better require a scheduled update or they explode. Everyone with an access to internet gets one. For the scheduled bomb update, you need to bring the camera records and the screenshots from your computer. Basically, you separate the people to important and unimportant; the important ones are watched more intensely, but they are the only ones who get full access to various things.

(I grew up in a communist country, if that is not obvious from my writing.)

Is there any way to increase public access to therapy-client records from over 30-60 years ago? Is it a good idea to do this?

Good for whom. You can blackmail the people who are still alive. Some things from 30 years ago are no longer important, but some of them are, e.g. if you figure out someone's sexual orientation, etc.

How to best nudge people

Make it the default option.

How much power do elites have to take decisions that go against their local incentives and local culture?  For example if the prime minister of a country is in favour of declaring war

This assumes that the prime minister is the one with the power to make decisions, rather than e.g. their sponsor who also happens to have some blackmail material on them.

Yes I am biased lol, I think most elites don't do anything interesting with their lives. 

Sounds plausible to me, but I have no first-hand experience.

unethical in the context of a research experiment. What are some techniques to bypass this?

Do the research in China?

Why didn't the US nuke USSR cities immediately after nuking Japan to establish a nuclear monoppoly, before USSR got nukes?

John von Neumann was in favor of nuking USSR a.s.a.p. "If you say why not bomb them tomorrow, I say why not today? If you say today at five o' clock, I say why not one o' clock?"

I think that USA was full of Soviet spies and "useful idiots" those days. People in the West back then had no idea what life in USSR actually looks like. They were incredibly (from today's perspective) naive about Soviet propaganda; they basically assumed that if the Soviet government says something, it must bear at least some resemblance to the truth (maybe an exaggeration, but not a complete fabrication). So they assumed that USSR was basically a workers' paradise (with an occasional egg broken here and there to make the omelette). It didn't help that USA chose to ally with USSR against the Nazi Germany, so the crimes of USSR were further downplayed for the sake of preserving the alliance. In such situation, it wasn't too difficult for USSR to find leftists willing to betray their own country for a vision of a workers' paradise everywhere.

Basically, imagine the people who take their information from Russia Today these days, except imagine that this would be what most of the smart people are doing, because they have no information that would contradict it.

Should I just stop caring as much about grammar and spelling in my writing, and invent more shorthands?

Only if you don't want other people to read and respond.