If you are actually on the phone and talking about the number you just dialled to achieve that call, then you would not say ' I had called on that extension but I was connected to this extension', you would instead say 'I did call on that extension ...' or 'I called on that extension ...'. This would indicate that the action of calling the number was recent and linked to the current call.
By saying 'I had called on that extension' makes it sound like a previous call that you made and not related to the current call.
The rest of the conversation is fine in regards to past tense.
As you said for yourself, there is relevance to the present situation. So grammatically present perfect would come there.
Why did the person emailed me "I did not forget you" [...]?
Well this maybe because he is not a native speaker. Or he might have thought no-one would notice the mistake or the slip-up. Or he might have thought that this is the correct tense (even after being a native speaker). Anything could have happened. By the way, the correct sentence should be:
Why did the person email me "I did not forget you" [...]? (Simple Past for emailing instance)
When reporting it to someone else, you could use either of them¹ did not forget or had not forgotten, given the first person said it in simple past tense: "I did not forget you"
He had emailed me saying that he did not forget me/had not forgotten me. (Past Perfect for emailing instance)
However, if the first person wrote it like: "I have not forgotten you", then you must use had not forgotten. This is called backshifting the tense.
He had emailed me saying that he had not forgotten me. (Past Perfect for emailing instance)
¹ Here is one reference site where it is stated that simple past in reported speech could take either simple past or past perfect (refer to the table). But there is ambiguity in the context then. The third person would think the first person said it in simple present tense which you converted into simple past tense or simple past converted into simple past tense.
However, this is the only site I could find which follows such rules. Majority of the site say otherwise.
According to this and this site, simple past goes into past perfect, no exceptions. But then again, past perfect could mean the original sentence was either in present perfect or simple past.
Conclusion: This is particularly an ambiguous topic in itself. Although people would rarely notice any omission or slip while in a talk, it may matter in educational outcomes and written format.
Best Answer
I think it's because the act of inviting and the act of giving (or in this case, forgetting to give) the address would've happened at the same time, meaning you'd use the same verb tense.
Usually "had + past participle" is used when that action took place before the simple past verb action. As in:
I invited my friend, and before that I had eaten dinner.
But it doesn't quite make sense to have forgotten to give your friend the address before doing the inviting. Clearly you forgot to give the address at the same time you're doing the inviting. And, evidently, you continued to forget to give the address for every moment afterward.
So in a very wordy way, I think the idea is:
I invited my friend, but later I realised that, while I was in the process of inviting him, I forgot to give him the address.
However, if I didn't know "A" was the right answer, I would've put "B" myself. I think this is the reason for why "A" is right, though. You can't forget the address exclusively before doing the inviting. You forgot possibly before (depends on if the invite was premeditated or impromptu), certainly during the inviting, and definitely after the inviting.