Learn English – So, “Would have + PP” or “Would not have + PP” only refers to unreal events, right

Yes, this is acceptable.

Both your sentences present conditionals; although they are not expressed as formal IF ... THEN constructions, they might easily be so:

The situation would have been worse if he hadn't helped.
It would have caused us a lot of problems if anybody had not cooperated.

The protasis (IF clause) of a conditional may lie outside the sentence at hand; this does not invalidate the use of would:

It looked like the school might have to close. That would have been a shame. = If the school had had to close, it would have been a shame.

All of these uses are equally valid with non-past^✲ reference:

The situation would be worse without his help.
The lack of anybody's cooperation would cause us a lot of problems.
It looks like the school may have to close. That would be a shame.

In fact, most uses of would may be understood as implicitly conditional, though the actual condition implied may be very vague:

I would like a piece of pie. [eg, if you have any or if you would be so kind as to bring me one]
I would be happy to do that for you. [eg, if you were to ask me or if you need help]
I would never say such a thing! [eg, if the opportunity arose or even if I were provoked]

^✲ I should perhaps note that past modal + have + past participle , although it looks like a “perfect” construction, has nothing to do with the ordinary English “perfect”. It is, rather, the language’s workaround for the awkward fact that the modals can, may, shall, will may be used in their “past” forms with non-past (present or future) reference—which leaves them no convenient form for expressing the same modality with past reference. To accomplish that, we employ the “perfect” construction. It would have been is in effect the simple past of It would be.

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.