A lot of the official titles to do with politics and the state are in Irish. Nobody in Ireland says Prime Minister, Deputy Prime Minister or Speaker of the House. It's always Taoiseach, Tánaiste and Ceann Comhairle. Also, we always say Dáil Éireann or the Dáil, we never call it the Assembly.

Oddly enough, we still use the English words President and Senate (though Seanad is more common). We rarely say police, it's usually the Gardaí or the Guards in English.

I recently found out that Éire is the official name of the state in both languages. The term Republic of Ireland has no official status (unless you're talking about the soccer team).

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Táim ag foghlaim fós. Fáilte roimh gach aon cheartúchán.

In indirect questions (I think that's what they're called):

Standard: He asked me if/whether I knew her./I want to know if you'll come
Hiberno: He asked me did I know her./I want to know will you come

Are your Hiberno examples not just bad grammar?

Edited to add that I have just realised that that doesn't mean they are not examples of the influence of Irish on English in Ireland!

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if it's considered correct in one native dialect, then it's correct in that dialect - but of course it's wrong in standard English. But it's not wrong in the absolute.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

This one made its way to Southern [US] English, though probably from Scottish Gaelic, as filtered into the speech of early Scots-Irish immigrants, some of whom would have been only a generation or two removed from speaking Gaelic: "I'm gonna see, can I do that" or "He don't know, is it there or not", which retain the original Irish/Gaelic syntax with what are essentially two sentences run together, the second one being a question.

And, of course, there are other "Southernisms" of Gaelic origin: "There's not but three of them there" (Níl ach trí acu ann), and words like Mammy and Daddy.

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.

these come from Irish? Isn't it the other way round? Using -y / -í as a diminutive ending is very Germanic and not Celtic, in my opinion... Btw when Irish native speakers say Daidí they pronounce it exactly as the English Daddy (with the same English d-sound that doesn't exist in Irish except in words borrowed from English)...

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

If I'm not mistaken, the Southernism "carry" to mean "take" (as in "Carry me back to Old Virginny") is also of Gaelic origin. In North Carolina, you'll still hear people saying things like "Will I carry you to church on Sunday?"

Redwolf

But "carry" is "iompar" in Irish, but in Irish you rather use "tabhair" to say you take someone somewhere, so it would be a Gaelicism if it were "I will give you there", wouldn't it be?
I don't see what Irish expression "carry someone somewhere" could have copied... do you know?

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Yes, "carry" is another one. After parties in college, we always "carried" our dates home to their dorms by car).

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.

I'm not certain, but I think it comes from the verb beir, not iompair, as in duine a bhreith abhaile (to bear/bring someone home) or as in Beir leat abhaile! (Get gone home!" -- i.e. "bear yourself off home").

Also, as for Mamaí, Irish endings in -aí (Scottish Gaelic -[a]idh) are pretty common, actually.

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.