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".
Compare the following sentences:
Present time
- It's very dangerous in Metropolis right now. You can be beaten up for just looking at someone the wrong way.
- It's very dangerous in Metropolis right now. You could be beaten up for just looking at someone the wrong way.
Sentence (1) presents being beaten up as a live possibility, as something that does actually happen to people. Notice that we can analyse for just looking at someone the wrong way, as some kind of condition:
1'. You can be beaten up if you just look at someone the wrong way.
Sentence (2) presents being beaten up as a hypothetical outcome of the wrong look. It is not being presented in the same way as in (1). It doesn't necessarily say that people are being beaten up for looking at people the wrong way - although we might assume that they are.
Could in sentence (2), as already mentioned, represents this outcome as a hypothetical possibility, as opposed to a live one. We could rephrase it as the following hypothetical conditional:
2'. You could be beaten up if you just look(ed) at someone the wrong way.
Remember both of these sentences refer to the present or future time. The way that we interpret you here is quite likely to affect our interpretation of the sentence. It's also quite likely to affect our choice of can or could. If you means a person in general, we are more likely to use can. If you is being used to make the listener imagine themselves in that situation, then we are more likely to use the hypothetical could.
Past time
Let's move forward twenty years. Now if we wish to make the same kind of statement but about Metropolis twenty years ago instead of now, we need to shift the tenses back to indicate past time. Example (1) would now be as in (3):
- It was very dangerous in Metropolis in those days. You could be beaten up
for just looking at someone the wrong way.
Here we see could appearing as the past form of can. This past form of can still implies that people actually were being beaten up for looking at people the wrong way. It is being presented as a live possibility for people at the time. It has exactly the same meaning as can, but refers to a past time. It does not represent hypotheticality.
However, in sentence (2) we already have past tense could, where the past tense indicates hypotheticality. If we wish to keep this hypothetical flavour, but also indicate past time, then we need to shift the tense back further. We need to use a past perfect form as in (4):
- It was very dangerous in Metropolis in those days. You could have been beaten up
for just looking at someone the wrong way.
Sentences (3) and (4) could be construed as the conditionals:
3'. You could be beaten up if you just looked at someone the wrong way.
4'. You could have been beaten up if you ('d) just looked at someone the wrong way.
So if we see a past perfect form could have this most likely represents past time reference plus hypotheticality.
Hope this helps!
Best Answer
When stated after the event has occurred/not occured, it implies something (slightly) expected and pleasent came true/ the opposite came true. The expectation doesn't have to be something you were 100% certain of, it could be more like 60% (I think it is possible, but I dont know for sure). Tone of voice and emphasis will tell you which way:
A dissapointed voice means that the hope didnt happen. If any words are emphasized, they are the relevant part of the wish.
If the tone is happy, it means the wish came true.
Note that in the above, the statement was made after the event happened or the opposite happened. If stated before the event, then the speaker is expressing their desires. It can sometimes also be a request, but it feels a little demanding.
A more polite version of all three of these is the "could" version.
Because "could" is a form of "can", it feels like the situation is responsible, not the people.
Just as before, the speaker is expressing dissapointment, but is explicitly not blaming anyone.
This expresses joy, but makes it seem like they were doing you a favour. It's an indirect way to say thank you.
This is a polite request.
Anyways, for the non-requests versions, you can change the tense from simple present to present perfect (notice -> have noticed) and it means basically the same thing. But it adds the nuance that the wish coming true or not has some significance to the present.