A: Nothing on its own. You need a Digital Receiver with a CI slot. A Sky Digibox or FTA box is no use.

You need a non-Sky Pay TV subscription and the legal viewing card which inserts into the CAM.

Nothing else is legal in the EU.

A: Only if you have the legal viewing card paid for to the offical supplier and it only gets the channels you paid for. Getting a foriegn Tv subscription in Ireland may be difficult through Legal Channels.

Check with the Pay TV provider. You may have to take out the subscription in a particular country or geogaphic area. Or for non-EU subscriptions, have the correct Nationality.
BBC Prime will sell to Ireland but not UK! (Though why you would want it with free BBC TV from Sky platform is a mystery)

A: Other than BBC Prime, none that are very appropriate to English only speakers or residents in Ireland. Check "packages" on Lyngsat Atlanic and Europe and contact the pay TV providers direct.

Google also is your friend.