Yes, rugby union is played in Ireland
Yes. Ireland is one of the world's leading rugby union nations.
All-Ireland League - rugby union - was created in 1990.
Ireland has many rugby teams. However, what you are probably referring to is why there is not a Republic of Ireland and a Northern Ireland team. The reason is that, like many sports in Ireland, rugby is played on an all-Ireland basis and there one organisation that looks after it, the Irish Rugby Football Union, and so there is one international team.
As of 2014, Ireland has never won the Rugby Union World Cup.
The Ireland National Rugby Union Team.
Its the IRB (International Rugby Board)
Fiji is the shortest registered rugby union team. Arguably the USA but that is an abbreviation.