I would say that the verb here in English could also be in the plural "Ireland win..." as in this headline from RTÉ: "Ireland win Six Nations title as England fall short on dramatic final day", where both "win" and "fall" are plural although their subjects are grammatically singular.
It is never "EIRE", it is only Éire with an accent on the fIrst É. That accent isn't optional, as eire without the accent is a completely different word.
Éire is the official name of the country in Irish. "Ireland" is the official name of the country in English. EU documents written in English only refer to Ireland as "Ireland" - see the list of member states on the English language version of the EU website, versus the same list in Irish.
Irish is legally the first official language of Ireland, and the Irish language name is used on the passport, on stamps and on coins. While certain other Irish words are used in English (Taoiseach, Dáil, etc), Éire is not used in English.
It may seem confusing but Knocksedan has outlined why Eire isn't correct; it not being the same word and it being a 'contested English' word. It would be similar to going around calling Scotland Alba(in) when writing or speaking in English.
Only it's likely considered (by many Irish people) to sound much more offensive as I would assume it would only sound odd for a Scot to hear Scotland called Alba.
If 'some' Irish people dislike the term 'the British Isles', 'almost all' Irish people dislike 'the English word' 'EIRE', given Éire is the geographical name for the island of Ireland in the Irish language while it can also be used as the name of the country, the ROI, in Irish. Ireland is the official name of the ROI used by the state and its people when speaking in English.
Using either 'English term/word' would be highly contested as both are inherently political. This can be highlighted by the fact that most British news publications have a style guide establishing what NOT to call Ireland, i.e. EIRE. Using it is either a sign of ignorance, hostility, or passive aggression.
Of course, ignorance is easily understood as many political Irish words are in the English lexicon and are therefore, uncontested, e.g. taoiseach. It should be somewhat self-apparent why one is problematic and the other not.
Calling the Taoiseach the Irish prime minister isn't going to ruffle any 'real' feathers but calling Ireland EIRE is a whole different ball game.
You have to add the Irish keyboard and switch to it for this to work (at least in Windows). For US users, using the default ENG-US keyboard, Alt-Gr is the same as the other Alt key - it won't give you a fada! But it's definitely worth adding the Irish keyboard - it makes it much easier to complete the exercises!
Really? It doesn't get any more informal than Twitter and I see gaeilgeoirí using Éire all the time. I doubt it's simply because it's fewer characters.
Keep in mind also that it's hard to say anything like that is the rule of thumb for all speakers, giving the divergences in colloquialisms among the dialects, between older and younger speakers, and even among Gaelteacht speakers and urban speakers.
If it is, I assume its a dialectical feature and I'm unsure which one. I think Scottish people use 'Albain' as their subject form in Scottish Gaelic while in Irish/Gaeilge that would be its dative form.
I guess phrases like Éirinn go Brách (Ireland forever) highlight that the dative is or can be used/heard in this way (also, I'm a little unsure how we parse verbless phrases?)
But I assume these phrases are somewhat political or if not, then at least 'sporting', and would assume they would be used by English speakers who have a few words of Irish.
In the standard, i.e. in standard written Irish, I'd assume using the dative in place of the nominative would almost always be wrong, with the exception of certain phrases, like the one above, even then it may be preferable to write, Éire go Brách.
I'd be interested for clarification on this from native speakers though?