The doctrine of the trinity remains an ambiguous topic. There are some ongoing discussions about the role jesus plays in the trinity (1,2); I am seeking clarification on some other points of trinitarian confusion, primarily in regard to the 3rd member.

1) What exactly does the holy spirit do, which cannot be accomplished by the father and son?

2) If the holy spirit is the one who impregnated the virgin, then why is the father called “the father”?

3) I’m assuming that the son and the holy spirit always existed, alongside the father. Had man not sinned, would there be any need for them? Did they serve any function prior to the creation (and fall) of man?

It would be good if these get clarified before anyone tries to tell us again why “the Blasphemy Challenge doesn’t work.

Thank you in advance.