I think what the page meant by saying "when, where, who" is that the perfect form doesn't go well with expressions suggests a particular time. The example sentences given at the linked page seem to be all about it.
The default past tense is the simple past, as Michael Swan says in his Practical English Usage (§421.4 "In general, the simple past tense is the ‘normal’ one for talking about the past; we use it if we do not have a special reason for using one of the other tenses.")
The perfect forms are needed basically to add the sense of completion to non-finite verbs such as infinitives, participles, and modal verbs. Because such tool exists, it's also used to talk about past events, but it ends up saying 'up until now' ('up until sometime ago' when it's the past perfect). Because it's tenseless by itself, it makes the sense of time vague, thus it has the sense of duration at the same time it conveys the sense of completion.
The use of the perfect forms are more to do with meaning than tense. Grammar books usually says it's one of tense form, but actually it's not about tense. Linguists call it 'aspect'.
The perfect form goes well with expressions like already, recently, just, since, ever, never. But it doesn't go well with expressions of particular point of time, when, such as yesterday.
I've read something more relevant to the OP's question, in the same M. Swan's PEU:
§457.1 (...) we usually prefer a past tense when we identify the person, thing or circumstances responsible for a present situation (because we are thinking about the past cause, not the present result). Compare:
Look what John's given me! (thinking about the gift)
Who gave you that? (thinking about the past action of giving)
Also
PEU §456.5
We normally use the present perfect to announce news. But when we give more details, we usually change to a past tense.
There has been a plane crash near Bristol. Witnesses say that there was an explosion as the aircraft was taking off, ...
There is rather a lot wrong with your text, I am sorry to say.
"I took the test...": nothing wrong with that.
"I think, I was well done." You can ask for a grilled steak to be well done, but in this context "you" is the subject of the sentence, and you think you "did well".
"I was hopeful and I hoped to pass it": OK, but stylistically it is odd to repeat the hope word. "I hoped to pass it" on its own is fine. "I was hopeful that I had passed it" is also OK.
"I shouldn't have expected it" is an idiomatic sentence, but not I think quite what you mean. I think you mean to suggest that you were surprised by the result of the test. If that is what you mean then one idiomatic way of expressing that thought is to say "I had not expected it".
You, might, however, mean to say that your hopeful expectation of passing the test was a mistake. In that case you could say "I should not have expected to pass".
Best Answer
Both of those sentences could be formed without other.
Although some native speakers would use other there it is unnecessary, and even a little jarring on a semantic level; in the following pattern, however, it is less jarring, though still unnecessary:
Only Usain Bolt is faster than he is.
Only Usain bolt is as fast as he is.