Prepositions – Help on / with Something

You're making me work! :) You could indeed use "of" in some of these examples. Some of them, we simply don't, some of them have a slightly different meaning, and some of them you could use either. Some of them I'm not quite sure of, because I don't have specialized knowledge of financial terms.

The first one probably could substitute "involving" for "for". The second one means that the framework is intended to cause more resilient banks. If you used "of" the banks themselves would be the framework. The third one could use of, but we generally say for in this case. The same for all of the sentences in your fourth paragraph, except the last one; we would never say "the world record of the 100 meters."

"The result for the debate" would be less often seen than "of" as you have it here, but it might be used. "A national shortage for teachers" would mean that there was something unspecified that teachers had a shortage of, for example "A national shortage of pencils for teachers". Future credit losses possess a present value, therefore "of" is correct here. The same for companies' credit spread changes. If you used "for" here, you would be saying that credit spread changes didn't belong to companies, but existed independently on behalf of companies in some way. Scenarios possess examples, so of is correct here.

The use of prepositions in any language is often arbitrary, and when they are they have to be learned by rote.

[Edit] I'll address your last question here. This isn't perfect, but it might help to some degree. "A for B" has a general meaning of A being in the service, under the control, or a part of B in some way. "A to B" has a general meaning of connecting A and B, with A the agent of connection (a "vector" exists from A to B, if you will). "A of B" means that B owns A in some manner. As you can see, these explanations overlap to some extent, which is why some expressions are idiomatic and have to be learned, and some expressions can substitute for, of, and/or to.

"Severity for external fraud" should be "severity of external fraud". The fraud "owns" the severity, and the severity isn't in the service or under the control of the fraud. "A key ingredient for the success" could be right, and you could also use "of". "An important decision for operational risk managers" seems best to me, since the decision is under the control of the managers.

Here is a list of ways in which for is used which may also help.

TL;DR: "at school" and "in school" are basically the same. You won't get yourself into trouble by using them the same way. This is almost always true when the verb is "learn", except for one corner case that I'll discuss below.

The long answer is that "school" can have several different, but related, meanings, and sometimes it sounds better with one or the other preposition.

In the example sentences you gave, "school" is a metonym that refers to the act of attending classes at some institute of learning. So "things you'll never learn [at / in] school" are things you won't learn by attending classes at some institute of learning. Any time that's the intended meaning, it's correct to use either "at" or "in".

On the other hand, sometimes you say "at school" to mean the actual location where the learning takes place. In those cases you usually have to say "at school" and not "in school". If you literally mean that something is inside the school location, you'd usually say "in the school" or "in the school building".

The border between these two uses can be very fuzzy. For example:

"Where's Bob?"

"He's at school / He's in school."

If we say "He's at school", it implies Bob is at the school building (probably attending classes). If we say he's "in school", it means he's currently attending classes at an institute of learning. In the example I just gave, it doesn't matter, but then we have:

"What's Bob doing these days?"

"He's in school."

While not wrong, it sounds a bit odd to reply that he's "at school" in this example.

One more example, specific to "learn":

"He learned French in school" means he learned French from attending classes at an institute of learning.

"He learned French at school" can mean the same.

But:

"He learned those bad habits at school" means the location where he learned bad habits was the school. Here "school" is the physical meaning. If we say "He learned those bad habits in school", then "school" is metonymy; it means that he learned bad habits from the process of attending classes. It strongly implies that the classes taught him the bad habits, whereas "He learned those bad habits at school" doesn't. The simplest way to understand this distinction is probably: If a professor taught him bad habits, he learned them "in school". If other kids or the janitor or random people who walked onto the campus taught him bad habits, he learned them "at school". If a professor taught him French, he learned it "in school" or "at school". If his French girlfriend taught him French, he learned it "at school". This is the only case I can think of where it makes a difference whether you learned it "in school" or "at school".