Re: Republicans
Ordinary republicans in normal sense that want constitutional unification by consent are "Nationalists".
Traditionally "Republican" in Capital R sense is those that LOST the Civil war and don't accept the partition of 1921, the anti-treaty people. Since the 1950s "Republican" means anyone wanting the 6 UK Counties added to the 26 by ANY means possible. Fianna Fáil also known as Fianna Fáil, The Republican Party were on the "losing" side. Technically SF is really Provisional SF, the political wing of Provisional IRA, a splinter from the Official IRA, a Northern splinter of part of the Anti-treaty of 1921 side.
Some long while ago Fianna Fáil became The republican party as they agreed to abandon the Territorial claim to the Northern six counties. Only SF is now a "true" Republican party in the bizarre Irish sense of the word. They make the Tea Party, Trump, Palin etc look logical. They are in reality run by the IRA Army Council in Northern Ireland (the bit in the UK).
The last Irish High King was nearly 1000 years ago and the coronation stone was lent to the Scots, who managed to let the English take it to Westminster. No-one in Ireland's 26 counties has been wanting a Monarch for about 900 years.
Republican thus, like USA, doesn't mean what you think. Though the Irish ones are left wing and think Stalin, Cuba, Libya, PLO etc are great.
SF stand for Election to Westminster. They do not swear the oath, nor recognise the Government of UK. Till very recently they didn't recognise the Irish Government either. I'm not sure given recent comments about Supreme Court that they really recognise the Irish State.