Shalom, hebrewdiva!
And welcome to SR!
I'm not in AA, so, I cannot address some of your questions specifically.
But, as you are aware, the commandment to save a life is foremost and above every other commandment. That includes your own life! So, abstaining during Pesach and the Sabbath is a necessity. Your life is at stake here if you are an alcoholic. Far too many alcoholics never return to sobriety after a relapse. And our religious traditions are no excuse for a relapse. I know of no rabbi, not even the most orthodox, who would say you must drink during these festivities -- no, not even during Purim!
I have, and occassional still do, go to alanon or naranon meetings, though. My son is a heroin addict. So, I understand what you're saying as far as my understanding of a HP and the Lord's Prayer. This is what *I* do.
My HP is G*D. I have no problem with G*D whatsoever. G*D is the Creator; the Eternal One; the Breath of Life within each of us. Jewish tradition speaks of G*D on many levels, and you shouldn't have any problem finding your HP within the Jewish tradition.
The Lord's Prayer does present us with a problem, I understand. We do not accept Jesus as the Christ, Greek for the Savior. We understand, and respect that others do, just as we know others respect our beliefs. So, again, what *I* do is just stand quietly during that prayer. I cannot pray to a god that is not true to me, even as I do respect others beliefs.
I must be true to me, first and foremost. To do otherwise would be harmful to my integrity. As Shakespear said, "To thine own self be true." As long as we are respectful and true to ourselves, we will continue to be respected. Afterall, we're there at the meetings for a common purpose, yes? And that purpose is support. So, keep it simple. And be true to yourself. You'll do fine.
L'Chaim!