Get you, Eire is simply a concise way of saying Southern Ireland. I take it you think everyone's a cretin who has a different POV? Ireland, as in Southern Ireland have a choice and those first two are perfectly valid choices although unlikely as their rulers won't let them anywhere near the option of leaving the EU. They also don't want a unified Ireland as even the Catholics in the North see they're onto a good thing with the >£10bn per year subsidy they enjoy. Southern Ireland can't afford integration financially, politically and socially
Integrating East Germany was much harder, EU will help in this case
Eire leave the EU and agree a customs union with the UK.
Eire leave the EU and re-join the UK.
Eire agree with the UK that they’ll police each others border with real checks at external ports and simple electronic passes for freight at the internal border and with an open border for citizens on the ground in Ireland.
I think the last will happen because there’s no way Eire will erect bricks and mortar border posts on the 1st November