I've got to hand it to you mate you've open a HUGE can of worm here and thats just the start.
Heres my answers to your questions,
Why is Irish music so strong in Ireland, is there no other music played in Ireland?
Well to state the obious Irish music is played most in ireland because the music is Irish. It may make more sence to ask why Irish music has had such huge success commercially and on a world wide level. In many countrys like sweden and denmark they also play Irish music well. I can't answer that you will have to ask some swedes about that. In Ireland and every country they always have more than just their music being played. I am English but I do not play strictly English music I have an International reportoire.
The national spirit and how it comes out in the music?
I do not know about this as I am not big on the political side of things so I can't help much there
I'm also lost on the gaelic as well
I hope I have been of some help, they sound good programs I hope they go well.
Cheers, Sam