Specific Questions
How to combine "She was/wasn't at home" vs "She had/hadn't been at home" with "when I called her"?
Without further details, these two forms effectively put her in the same place at the same time. More below under "When was she at home?"
Does had been at home mean that she was at home up to the instant in time I called her?
No, "when" is not the same as "up to" or "until." The "when" in this sentence means she was home exactly when you called her. A different description would be grammatically correct to say that, such as "She had been home until I called her" to mean that she was home up to the moment of your call, but that also doesn't anything about that moment itself. She could still be there or could have just left - you're not stating anything about her location at that time.
Subordinating conjunctions
A subordinating conjunction (when, before, after, once, until, whenever, since, while) along with a description is often needed to complete the meaning by specifying the duration or moment in the past tense. This description works together with the verb tense itself. Further, each conjunction only covers its own moment or duration, and says nothing about other moments or duration.
For the last two paragraphs of your question, I'll step back and look from a few angles.
Moments in time / Had been SOMEWHERE
"Had been somewhere" can mean either past perfect (a single moment or occurrence) or past perfect continuous (a span of time or multiple occurrences). To distinguish that requires more description:
(past perfect) "I had been to that park only once, before deciding the extra walking is worth it to go to this nicer one."
(past perfect continuous) "I had been in Italy for three years by then."
When was she at home?
"She had been at home when I called" has the same effective meaning about her location at a specific time as "she was home when I called" -- that is, there is no direct meaning about her location before or after the time of your call. She could have just gotten home while the phone was ringing, or been home for days. Rather, "she had been home" suggests that you might be about to describe another moment when she was not home. For example, it would be natural to use past perfect tense before describing a contrasting later moment, such as: "she had been home when I called her, but she was not there when I arrived to meet her" or "she had been out shopping, but she was back home when I called her." (Still, in those examples, the simple past "was home" or "was out shopping" would also be grammatically correct and feel natural to hear or read.)
For simple cases like where someone was at one moment in time, there's not a strong reason to use "had been." However, if there is one or more later moments that are different from this moment, the past perfect "had been" will help the reader or listener prepare to receive and understand that distinction; it helps to indicate that a change is about to be described.
More generally, past perfect can be used to indicate a past moment or interval that occurred prior to another past moment or interval. The Grammarly post linked below highlights another distinction: simple past can possibly mean the subject was in the habit of normally doing something.
In native speaking
There are certainly differences across the native English speaking world regarding how past perfect or simple past tense is used, and in some cases these don't strictly adhere to established grammatical rules of English. There is some complexity induced by this, but overall, the context provided by subordinating conjunctions is key for conveying the meaning, especially establishing a moment or duration, which is anchored in time by that additional information.
Further reading on tenses:
Aspects of the Past Tense
https://www.thefreedictionary.com/Aspects-of-the-Past-Tense.htm
Past perfect (with comparison to simple past)
https://www.grammarly.com/blog/past-perfect/
Past perfect continuous (also called past perfect progressive)
https://www.grammarly.com/blog/past-perfect-continuous-tense/
Present perfect continuous / present perfect progressive:
https://www.grammarly.com/blog/present-perfect-continuous-tense/