modal-verbstense
could have vs would have
I know could means indicating a possibility or ability, and would means the past of will or something about that is uncertain.
Which of the following is correct?
If you had told me, I would have used the other route.
If you had told me, I could have used the other route.
Both of the above sound correct and similar to me.
Are these also possible?
If you had told me, I would use the other route.
If you tell me, I would use the other route.
Please clear my confusion.
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
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
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.
"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.
"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.
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
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".
"Could" is the past tense of "can", so let's start with "can".
"Can" has a number of meanings (see M-W). It can indicate possibility:
Do you think he can still be alive?
It can also refer to ability:
He can lift 200 pounds.
"Could" has similar meanings but the time frame it refers to can complicate things. If you are referring to possibility, that's the same in the present:
He could still be alive.
Using "could" for the present perhaps adds a nuance. "He can still be alive" is sort of a yes/no statement--either he is or he isn't. "He could still be alive" implies that his status depends on conditions.
If you are talking about present ability, "can" is definitive:
He can lift 200 pounds.
This means that he definitely is able to do it. "Could" is conditional; there's an "if" or a "when" or other conditional term that modifies or limits the statement of ability. For example:
He could lift 200 pounds if he recovers from his injury.
Take the example in the question:
...a few Air Force helicopters could [not] achieve much
Without the surrounding context, this might have potentially referred to the present or future. In that case, the meaning might be referring to either possibility or conditional ability, depending on the context.
The potential meanings of "could" change when referring to the past. The action has already happened, so whatever possibilities there were have already played out; they are no longer possibilities but a specific reality.
He could lift 200 pounds.
This means he definitely was able to do it in the past.
Returning to the example in the question:
...a few Air Force helicopters could [not] achieve much
As a past reference, this refers to what actually happened. The helicopters did (or didn't) achieve much.
"Could have" (done something) is used for saying that something was possible in the past, even though it did not happen. (Macmillan} Example:
You could have been killed.
If it had actually happened, you would use did, were, or a similar "actually-happened-in-the-past" word. Could have refers to a prior possibility whose time has passed.
Since could have means that it did not, could not have might seem like a double negative (what, exactly, is being negated by the "not"?). Here's why that isn't the case. The "could" portion refers to what was possible (or an ability). The "have" portion refers to completed action (the perfect; see M-W). Modifying "could" with "have" is what says that the "could" did not happen.
So could not have still refers to something that did not happen, but the referred-to action was a "negative" possibility; i.e., lacked the ability to happen (and the "have" means sure enough, it did not).
The example in the question:
...a few Air Force helicopters could not have achieved much
This refers to something that did not happen and (or because) it lacked the ability.
Best Answer
Would here denotes a certain consequence of the unreal condition: no question about it, I would have used the other route.
Could denotes a possible consequence of the unreal condition: if you had told me, I might still have taken this route but I would have had the choice of taking the other route.
These are not quite impossible, but the circumstances under which either would be acceptable are very unlikely to arise. Ordinarily these forms would be understood as having the tense/mode significances I have noted in superscript, and in most cases the two verbs, the one in the IF clause and the one in the THEN clause, should have the same tense and mode.†
† This is not always the case in conditional clauses involving logical inference; but I do not think either of these sentences can be read as inferential.