You don't need to submit it separately to Google.ie. If one Google site knows about your site, then they all will. If your site is doing well in Google.com but not showing up in Google.ie, that's probably because Google (rightly or wrongly) considers that the site doesn't meet the needs of Irish searchers.
No, there is no separate Google Webmaster Tools (GWM) or Analytics for the different Google sites. If you register your site with GWM, the figures you see will be an aggregation for all countries. You can then filter by country to see the results separately for Ireland of you wish.
If you want to improve your performance in Ireland, you can use GWM to tell Google that the site is targeted specifically at Ireland. That might or might not hurt your performance in other countries. You will need to monitor the results carefully, and reverse the action if necessary. A better approach might simply be to add some content that is of particular interest to Irish visitors.