Translation:I am afraid our parents are calling us.
Possibly, but not in this case. It would be rather odd for someone to refer to his/her own parents as "i genitori" and not as "i nostri genitori". This sentence could be used by teachers after teaching controversial subjects to students.
It's like "The old lady" instead of "wife". You wouldn't use it for anybody else. And if you had to, you would be explicit. (I think. I am only level 12)
I hate these sentences at this point, because I understand them, but I can't express them in English. Ahhhh.
Yes. That's how I interpreted it. As, for example, a teacher talking about his students' parents. I spent a few seconds trying to decide which helping verb would be best. I settled on "I'm afraid that the parents will call us," which was not accepted.
Not really. Italian would specify "miei/tuoi/suoi/nostri/vostri/loro" exactly as in English.
To a native speaker, which of "the" "my" or "our" parents would be the most likely interpretation here? And for the other two, would you include "miei" or "nostri" to clarify?
Neither 'my' nor 'our' in this very sentence. The possessive is not used, which means that the parents in questions are not mine/ours (exactly as in English).
The use of miei or nostri is connected with the context. If I am talking with anybody but my siblings, then it would be miei; otherwise nostri.
It becomes easier and easier for english and non latin speakers, as they learn other languages as Portuguese, Spanish, French and other latin languages, I can tell because my mother language is Portuguese, and I have similar problems with languages like German, English and Dutch.