The Irish border is a problem for EU to sort out not rest of UK, which will keep the border as open as possible, don't know why Irish are worried about borders as 80% + of their exports are to rest of Great Britain.
Just wow. I don't know where to start with that one.
1. There is already a border (government, different laws, VAT, customs and excise - think fuel, tobacco, alcohol).
2. UK will have no obligation to police the border except and unless UK wish to. They have said they do not wish to do so e.g. no hard border.
3. When UK leave the EU, Ireland has a contractual obligation to the EU to police the physical external borders of the EU, i.e a hard border. This is more than a little awkward for the Irish Government although in the Good Friday Agreement they did give up claim to Northern Ireland.
The bilateral Good Friday Agreement covers the issues of nationality and free movement of people living in Northern Ireland. Also Ireland and UK are the not members of the EU Schengen Area Agreement because of the bilateral UK/ Irish Common Travel Area. So free movement on the island of Ireland is not an issue, nor is movement between Ireland and UK except for the EU.
Incidentally, by default, after we leave the EU a Northern Ireland citizen would still be able to be all of a UK, Irish and EU citizen as they wish.