These are all meaningful, but the meaning is changed and the context in which they could be used would be changed. "Would" is more often used to discuss expectations (that one feels certain about) in projected courses of action, rather than hopes or expectations in the current situation. You wouldn't use "would" there except in limited circumstances, when you are very confident in your predictions. I think a lot of this falls out of the use of "should" to describe model behavior or what is 'right' (like def. 3 here). Incidentally, I think (without proof) that that is why we don't use "should" to describe expectations that go awry, like the train being late: we certainly don't think that our hopes or expectations ought to be denied!
with "should" is a prediction; with "would" the speaker is certain enough to, for instance, discount the possibility of it not having been received. ("They would have it by now, so that can't be the reason they haven't responded...")
"should" states a probable expectation, while "would" is more like a certainty in a hypothetical plan ("We would get there by six, which would give us time to change before dinner...")
is tough. "We wouldn't have to wait much longer" is an acceptable utterance with an appropriate context: if I'm making a case for my plan (staying in line) over your plan (leaving the line). The implied full thought is "we wouldn't have to wait much longer [if we agreed to stay]." Here we are discussing the expected-to-be-certain details of possible plans, rather than stating our hopes about the future.
would work if you'd said "there were no reports of delays, the train would be on time [and that is why I am worried that your sister hasn't arrived yet]". This is related to sentence 1; I am stating a prediction about which I feel certain enough that I discount the train being late as a possible reason that your sister is delayed, and start worrying that something else could have happened to her.
Meaning is completely changed--we don't use "should" to emphasize things that happen contrary to expectation. Sometimes "The train would be late!" (with emphasis) is used expressing frustration that the train is late. The resulting statement is whining. A more full example: "The train would be late on the day I have an interview! This always happens to me!"
So: the distinction as I see it is pretty much what your edited addition says. "Should" suggests a more tentative attitude than "would," which may be from genuine uncertainty, or from an attempt to be more polite or more emotionally removed.
Both "should" and "would" are used to discuss an event about which the speaker is not completely certain or confident. But "would" seems to have the implication of talking about the details of a hypothetical world, future course of action, proposed plan, etc. "Should" is used to make less confident predictions about the future.
I was hoping ~
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:
I was hoping he'd pick me... (he picked another person)
I was hoping you'd buy a large pizza... (they bought a small or medium)
A dissapointed voice means that the hope didnt happen. If any words are emphasized, they are the relevant part of the wish.
I was hoping you say that!
I was hoping he'd be here.
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.
I was hoping you would take a look at my computer
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.
I was hoping he could make it to the party... (but he did not make it, maybe he was busy with work)
Just as before, the speaker is expressing dissapointment, but is explicitly not blaming anyone.
I was hoping you could eat with us (as they are all at dinner together)
This expresses joy, but makes it seem like they were doing you a favour. It's an indirect way to say thank you.
I was hoping you could help me with my homework
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.
I was hoping you would have been home (but since you are not, you will miss Game of Thrones)
I was hoping you'd have known the answer (and because you did, you were able to tell the answer to me, yay!)
Best Answer
No, "should" is not generally interchangeable with "would". The easiest rule of thumb is that when a speaker uses "should" she is prepared to explain why, and when a speakers uses "would" she is prepared to explain why not. Here are some examples:
With "should", the speaker always has a reason why something did/will occur. If the speaker's reason [in brackets] isn't explicitly stated, it is still implied. Now consider "would":
With "would", the speaker always has a reason why not - why something did not occur. The speaker is more likely to explicitly state her reason [in brackets] with "would". If we are using a future tense, the why not rule of thumb becomes awkward but still workable:
In sentences like this, everyone understands that it is hypothetical, so the speaker would rarely actually say the reason in brackets [if this hypothetical situation ever arose]. (See what I did there!)
One final note, which makes this kind of tricky, is that you can still use "should" even when you state a why not reason as long as a why reason is still stated or implied:
Actually means:
So in sentences like this, "would" and "should" are almost interchangeable. Just remember that "should" means the speaker knows why and "would" means the speaker knows why not. If the speaker happens to know both, then she can choose "should" or "would" almost equivalently.