1) Yep, Long Stay (D), Employment visa. Just make sure that, when you get the visa, it says type D (they issued me with a short-stay C visa, but I only realized that when I arrived in Ireland, and am now going back and forth with INIS to correct it, ouch).
2) I was told by the consulate in my home country that I can only get a single-entry visa (which is what I went for), but I know a guy who left a few months before me, and applied (and got) a multiple-entry visa. I'd go with single-entry, to stay on the safe side, and the application for a multiple re-entry visa (once you get to Ireland) is only 100 EUR (and that one lasts as long as your Green Card).
3) Don't know, I never lived outside my country. I don't think your case is much different, though - my guess is they're looking for info if you've lived in other countries for prolonged periods of time.
4) Doesn't sound like your case falls under 'deportation', but I can't give you a correct answer.
5) It's fine that you say "No", I'd say. This question pertains more to people that are seeking visas for other purposes.
6) ACCA and similar don't count as full-time degree-granting programes. So, "No".
7) I just put N/A in all the address fields. I think there was an extra field, after all that, like "Other" or "Comments", where I wrote something along the lines of "Will be temporarily staying at a B&B while searching for permanent residence".
Yep, your Green Card number goes here.