Why does it not accept Éirinn?
It should, I was perplexed too. The discussions earlier pointed out that "Éirinn" is used by most speakers, I guess there was an omission here.
What is the difference in usage between "Éire" and "Éireann"?
Éire is Ireland but Éireann is the genitive i.e "of Ireland". The people of Ireland = muintir na hÉireann but " I live in Ireland" = Tá mé i mo chónaí in Éire / Éirinn.
The Irish passport has Eire on the cover right above Ireland, with the fada of course.
I learned this one from the disney movie Luck of The Irish XD
Ireland = Éirinn