The present perfect is not permitted with ten minutes ago.
As explained here, the present perfect is a statement about the present, not about the past. Consequently it cannot be used with temporal expressions located entirely in the past, only with temporal expressions which include the present.
Ten minutes ago locates the departure in the past, and therefore requires a past tense. Since the departure was completed at that time, not continuing, a verb in ‘perfective’ aspect is required; in English, that aspect is expressed by the simple past.
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 is (mostly) fine. There is no rule that says that all the verbs in a sentence have to be in the same tense. Sometimes the sentence makes more sense and reads better if the tenses match, but sometimes, like in your example, that wouldn't make any sense.
She went shopping - this happened entirely in the past, so the simple past is appropriate.
and
(She) hasn't come back yet - this began in the past and continues until the present, so the present perfect is appropriate.
When you think about it, there are lots of cases in which you would use different tenses in one sentence, e.g. "Yesterday I lost my glasses and tomorrow I will buy new ones" or "I had never seen an elephant until I went to the zoo, but I still haven't seen a tiger."
(The one correction I would make to the sentence is that it's using what's called a comma splice. "I lost my wife" is a completely separate main clause from "She went shopping and hasn't come back yet", and you can't join two independent clauses with a comma. You need to separate them into two sentences with a period, or connect them with a semicolon or a conjunction like "and" or "because".)