Irish Modern Dance Theatre was created in 1991.
Irish Literary Theatre was created in 1899.
Irish Times Theatre Awards was created in 1997.
Acting Irish International Theatre Festival was created in 1994.
Irish Museum of Modern Art was created in 1991.
Riverdance is a Irish step dance
No one person can be said to have created Irish dancing. There are many kinds of Irish dancing. It would have developed over hundreds of years, with many people adding new types of dance to what was there.
If what you are asking is What is the word for dance in Irish? It's damhsa [dhowsa] or rince [rink-ye].A dance as a function is damhsa, céilí [kaelee], or rince. For a short history on Irish dance see the link History of Irish Dance.The name for Irish dancing in Irish (Gaelic) is: rince Gaelach.
Jig or Irish step dance
Same reason any dance is - people enjoy it. Irish dance is a very beautiful dance.
I believe it is the Single Jig/Light Jig in Irish Dancing that was once a Irish Peasant Dance.
The Abbey Theatre in Dublin does have Irish plays very regularly.
McConoghmy School of Irish Dance