Shannon Info frequency for the whole of the Republic of Ireland (below FL75) is 127.5mhz. They provide a radar derived flight information service.
If under the Dublin CTA, then you'd use one of the Dublin frequencies rather than Shannon, but your description doesn't suggest that you'll be under the Dublin CTA.
When over NI, you can use Belfast City, Belfast Aldergrove, or Scottish info (Frequencies shown on the CAA chart).
As for customs, I'm not sure. All custom in Ireland is local agreements, so you should contact Donegal airport and ask what their arrangements are.
Donegal airport if nice, and ATC is very friendly (Don't let the class C put you off...it's not busy!). As Ryan says, there is a lovely beach right beside the airport. But apart from that, there is nothing else within walking / reasonable taxi distance.
You'll neither either friends with transport, a rental car (often cheaper to hire directly at the airport desk) or an awful lot of time and a definate plan of where you want to go.
dp