Could have is saying that something was definitely possible in given circumstances.
Could have indicates that the option was available: that the possibility existed, not limited by circumstances, situation or personal ability. It tends to be used when you are talking about an entire hypothetical scenario.
When I was training for the marathon, I could easily have beaten you in a race!
The focus is on the capability: in this case the speaker knows that they definitely could have won the hypothetical race if such a race had occurred.
Note that saying they are definitely capable of doing so doesn't necessarily mean that it would definitely have happened, just that it had a probability of more than zero. A negative example might help to illustrate this:
Even if I had trained for a year, I could not have beaten Jesse Owens in a race.
It also doesn't give any indication of how likely the speaker thinks the possibility was, just that they believe it was definitely a possible outcome.
Would have defines a definite outcome given different circumstances.
Would have indicates that something intervened to stop the predicted outcome from arising. It tends to be used when you are talking about a change to the real sequence of events: if something had happened differently.
I would have beaten you in that race if I hadn't tripped up!
This is expressing certainty: if the situation was different (in this case, not tripping up), the predicted outcome (beating you) would definitely have occurred.
Might have defines a possible outcome given different circumstances.
Might have is the same as would have, but the speaker is less certain of the outcome.
I might have won that race if I had done more training.
I didn't win the race, I think I might have won if I'd done more training, but I also think that I still might not have won even if I had done more training.
Your specific examples
As you might have guessed, many of these sentences are correct but with subtle differences in nuance.
Example B
- If I hadn't been so tired, I might have realised what was happening.
- If I hadn't been so tired, I could have realised what was happening.
Because this is talking about a change from the actual situation, not an entire hypothetical scenario, "might" sounds more natural here than "could". That doesn't mean that "could" is wrong, just that it would be more common to say "might".
If you were sure that you would have realised what was happening if you'd been less tired, you could say "would" instead of "might".
Example E
- Why did you jump out of the window? You could have hurt yourself.
This is indicating that hurting yourself was definitely an option (and hence it was stupid to jump out of the window). For this reason, it expresses the sentiment most strongly out of all your "window" sentences. It's implied that you were lucky not to hurt yourself - in other words, luck was all that prevented you from hurting yourself.
- Why did you jump out of the window? You might have hurt yourself.
"I suppose you might have hurt yourself, but I'm not a window-jumping expert, so I don't know..." There's less certainty here, so it's less forceful. However, it's still entirely acceptable.
- Why did you jump out of the window? You would possibly have hurt yourself.
"Would possibly have" has the same meaning as "might have". To me, it sounds slightly less natural here, but I think that's because the question itself sounds a little accusatory, so adding the "possibly" in is a little awkward.
Example D
You didn't suggest a substitution for D but I'm including it to show the difference from E.
- I was so angry I could have killed her!
- I was so angry I might have killed her!
In this instance, it's actually the "might" example that is stronger. That's because the "could have" suggests that the speaker was angry enough to kill her, but chose not to. Because it's "could", we know it's a hypothetical scenario and that there was no chance of him actually killing her: just that his anger gave him the capability of doing so.
However, "might have" admits the possibility that this outcome might actually have occurred. It sounds like it's something external to the speaker that prevented it, like someone walking in, or maybe he went so far as to beat or shake her and it was only luck she didn't die.
Needless to say, "would have" is therefore the strongest of the three, indicating that she definitely would have died if something had been different (like they didn't get interrupted).
Example F
- I could have won the race if I hadn't fallen.
- I would possibly have won the race if I hadn't fallen.
These both sound equally natural, but the nuance is different. In the first one, the speaker is certain of their ability to win races, but acknowledges that that doesn't mean they'll win every race they ever run. Falling stopped them being able to win the race - an ability they had before they fell.
In the second sentence, on the other hand, the speaker is still acknowledging that the outcome of the race (even without falling) was uncertain, but they are doing it in a way that includes the possibility they might not have won the race because they simply weren't good enough. It's a broader statement: that they might have gone on to win if they hadn't fallen, but they don't know if they would have gone on to win.
Some other things you mentioned in comments
I think your would possibly/perhaps have example is the same as might have, and would have been able to is the same as could have, with would have been allowed to being a subset of that where permission is the limiting factor of the "could".
The short answer is that, yes, you absolutely can use "would have" with past simple, just as you know you can use it with past perfect. When you learn English, you may well learn about 2nd conditionals (If + past simple, would/wouldn't + verb) and 4rd conditionals (If + past perfect, would have + past participle). You may not have learned that it is possible to mix conditionals. Oh the flexibility of language!
Let's see:
Rule of thumb: We use the 3rd conditional (as mentioned before) to describe past situations that we cannot change, whilst we use the 2nd conditional to talk about situations referring to the present time.
2nd conditional: If I were taller, I'd be able to see over that fence.
3rd conditional: If I had been born a giant, I would have dunked that 3-pointer easily.
So it stands to reason that given the right ingredients (or situation) we can mix up elements of these two language constructs.
To comment on the book quote you referenced, the structure is correct. Trisha was thinking (in that particular moment in the past) (hence past simple) it was impossible for me to turn up, however, as soon as I did, the reference to me not showing up became completely impossible, as shown by "wouldn't have shown up" rather than "wouldn't show up".
Unfortunately, this example
If you called me we would have gone for a movie.
is not right. Since the opportunity to call in that particular instance has passed, you can't use a reference to the present situation, but rather to the missed opportunity, like so:
If you had called me we would have gone for a movie.
Hopefully this has helped you, but I'll present a final example to see if we can really crack the case.
I am in a sweet shop with my five-year-old son. He's a bit mischievous and so with my back turned he tries to grab some sweets from a high jar, which smashes on the floor. In my embarrassed state I think to myself "If he were taller, he would have been able to grab the jar no problem."
I comment on the general situation (my son is not so tall) mixed with the (unfortunately) impossible to change scenario of a broken jar (he would have been able to grab the jar). Hence, referring to multiple aspects of time allow us to use a combination of tenses. Equally, I could have used a pure 3rd conditional:
If he had jumped higher, he would have been able to grab the jar.
Either way, we're not allowed back in the sweet shop.
Best Answer
1.If I needed more money in the future, I would have to do a better job.
Compare your sentence with: "I need more money, so I have to get a better job"
It is the same but yours is conditional, as you have said "only in the event A of would I have to do B".
2.Freddy sneezed on the cakes. He would have to go and do that.
This doesn't sounds right. Literally, your sentence means that Freddy was obliged to sneeze on the cakes. More normal would be:
"Freddy sneezed on the cakes. He would go and do that" - with emphasis on the would. The emphasised would here means that this is something typical of Freddy, because he is the kind of person who sneezes on cakes.
3.A: What did you do yesterday? B: I repaired the broken window. A: Ah yes, you would have to do that. Broken windows are dangerous.
Again in this example "would have" doesn't sound right. More logical here would be "should". Because repairing windows is something you should do, to prevent people injuring themselves. I tried to think of a logical way to write your sentence with "would have", and came up with:
"...Ah yes, you would have had to do that, because broken windows are dangerous". - That looks like quite a mouthful, but logically means "in the past, you were obliged to do that.