Irish and English law do share a common heritage, both descending from Common Law and the Courts of Equity. There are even some statutes that are still in force in both jurisdictions. However, since independence, the statute laws have taken their own paths, and even common law has taken differing paths, e.g. our tort law has gone more pro-plaintiff, and legislation has significantly changed the position also. England substantially reformed its Land Law in 1925, wheras we've only started in the last few years. On the other hand contract law is substantially similar. The vast majority of Criminal Law is statute driven in Ireland, and will differ significantly from England. Our constitution introduces a whole differet dynamic to the development of law since the sixties.
In short studying English Law would give you an awareness of Irish Law and its basic princlples, but not a familiarity with it.
As regards interpretation of EU law, they will be pretty similar since this comes from the ECJ, but the incorporation of EU law into national law differs significantly, not least because of our constitution.
Can't help you with the rest.