A conditional sentence has two parts: the "if-part", or protasis, and "then-part", or apodosis.
In the apodosis, we use would to create that "conditional" feeling. So the sentence
If we had had lots of money, we should have travelled round the world.
would be illogical: the protasis clearly says that we did not have money during some period in the past, but the second half of the sentence is not an apodosis, because it uses the wrong modal verb. The second half looks like a normal sentence on its own:
We should have traveled around the world! (instead of doing some other things in the past, we should have traveled around the world)
This clause implies that we had the ability to travel around the world. It contradicts the protasis.
The same applies to your conditional 2 example:
If I worked harder, I should pass the exam. [improbable situation in the present or future],[moral obligation]
The first part invites some apodosis with would. The second part just plainly states your obligation to pass the exam. But according to Wikipedia,
Occasionally, with a first person subject, the auxiliary would is replaced by should (similarly to the way will is replaced by shall). (Wikipedia says this about the apodosis of both the second and the third conditional)
So maybe we can use should there after all, since I is a first-person subject. Let a native speaker decide.
The use of should is usually "deontic" (what should be: used to express norms, expectations, speaker's desire) while the use of would is "epistemic" (what may be).
The modal verb should could be sometimes used in the epistemic mood too, so we can come up with sentences such as
If I worked harder, that should be surprising!
But the effect would be comical and ironical, not the usual effect with the conditional sentences. The two halves of the sentence would still look somewhat disjointed.
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:
Muskie should have won by a huge margin [because he is much better than the competition].
Muskie should win tomorrow [because he is much better than the competition].
You should have heard by now that I'm OK [because I saw the doctor talking to you].
You really should have started that paper more than 8 hours before it was due [because it's very difficult to write a quality paper in less than 8 hours].
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":
Muskie would have won by a huge margin [if he didn't blow his engine].
You would have heard by now that I'm OK [but you didn't buy me a cell phone, so I couldn't call you].
I would have started that paper earlier [if I wasn't so busy with all my other homework].
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:
I think she would like this as a gift [if we decide to buy it for her].
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:
Muskie should have won if he didn't blow his engine.
Actually means:
Muskie should have won if he didn't blow his engine [because he is much better than the competition].
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.
Best Answer
Should in sentence 1 is not the same use of should that we find in examples such as:
The sentences above are asking for advice or giving advice. We can think of advice here like a form of weak obligation. If someone gives us advice, there is some pressure on us to do that thing - but we don't have to do it - it is our decision. This kind of meaning, when we talk about obligation and permission, is called DEONTIC modality.
Sentence 1 is NOT about deontic modality. This type of should is about EPISTEMIC modality. Epistemic modality is about knowledge and belief. Think about the following sentences:
The first example above shows that the speaker has a weak belief that it is in box 3. The second sentence shows that the speaker has a fairly strong belief that it is box 3, but she's not certain. The last example shows that the speaker is certain that it is in box 3.
In the Original Poster's example, (1) indicates that the speaker has a strong conviction, a strong belief, that Monday will be fine. Of course this is the technical meaning of what they are saying. The effect of saying this sentence is probably "Yes, choose Monday".
Would in sentence (2) indicates a logical result of choosing Monday. The sentence is like the last part of a conditional:
Here the speaker is definite about the fact that the result of choosing Monday is it's being fine. They aren't indicating any doubt about it. Again the effect in the conversation is probably "Yes, choose Monday".
Hope this is helpful!