No, the answers aren't all Irish related. Very few are in fact. The clues tend to be extremely cryptic. I don't get the Sunday Independent, so I don't know about their crossword.
Clarification
There are two crosswords being quoted here.
Phoenix magazine of 30th November(closes 7th Dec.) and
Phoenix (magazine) Annual- Christmas crossword(closes 4th Jan.)For the benefit of those who may not have either ,can i suggest using a clear reference heading
Hope this is helpful