No. Apparently not. The relevance of Past perfect lies in the fact that it differentiates between the time frame of two events, when both of them happened in the past.
Example:
Before she left for her college, she had finished her lunch.
You can use After too. In the given sentence in your question,
Mario had already arrived home when his mother walked in.
it is understandable that Mario had reached home before his mother walked in.
BUT a simple,
Mario had arrived home.
is meaningless and unnecessary as you are not referencing before what event had he arrive home. You can use simple past here. Of course, if in a conversation it is relevant that you did it before some action you can use simple perfect like you cited. Like:
2nd friend: Where do you work now?
1st friend: I work in ABC company now-a-days.
2nd friend: Oh! I see. I had worked there. (It means he had worked there before he left that job)
So put it simply,
Past perfect is not used unless and until we are comparing the time frames between two events. You can read more on past perfect in English Page: Past Perfect Tense.
Let's first talk about the following two sentences:
1- Sara went to bed as soon as she had finished homework.
2- Sara went to bed as soon as she finished homework.
I think your confusion is valid because we use the past perfect when we talk about something that took place before another thing in the past. So the use of the past perfect comes across in the first sentence but the use of the past simple in the second sentence doesn't. Am I right? In fact, we don't need to use the past perfect unless it is necessary or unavoidable to do so. Even if we talk about one action happening before the other one, it is possible to use the simple past for both actions if we think it is not necessary to highlight or emphasize the happening of the earlier action. It sounds natural to avoid using the past perfect where the simple past works, which is used to refer to something or several things happening in sequence (one after another) in the past.
So both of the sentences are grammatically correct. However, I'll prefer the second phrase to the first one.
As for the last two sentences, it is correct to say that "everyone had gone home when Sara got to the party", but it's not grammatically correct to say that "everyone had gone home when Sara had got to the party". It doesn't make sense. In the past perfect when we talk about two events, we use the simple past in one clause and the past perfect in the second clause.
Let's now talk about the following sentence you are confused about:
"Everyone went home when Sara had got to the party".
There is nothing wrong with this sentence, but the meaning is other way round. It means that first Sara got to the party and then every one went home. Look at the
first sentence again. When Sara got to the party, everyone had gone home. Here it means that first everyone went home and then Sara got to the party. Sometimes, one action happens soon after the other action, here we should use the past simple in both clauses such as when Sara got to the party, everyone left, when they saw the police, they ran away, etc.
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Best Answer
The sentence "I've already done it last week." is wrong, since "last" is not used with the present perfect tense and because, as you have mentioned, the present perfect tense is used for an action which happened at an unstated time in the past. So if you want to say "when" you did something, use the simple past tense, as in the second sentence.The only case that we use the present perfect tense for an action which happened within a specific time period is when the action is not over at the moment of speaking.
e.g.I've written two letters this morning. (The time period is not over. It is still morning.)