That will depend on your nationality. You may live in England, but have a different nationality, so you would not have the same conditions of entry as someone who is has a British passport. See below for details on getting into Ireland.
Technicaly yes you can, but its not wise or advisable to try to come to Ireland without your passport, some airlines wont let you board a flight without a passport. To ensure that you travel with the minimum of hassle make sure to have your passport and make sure that its in date.
no you don't need a passport to travel between eire and the UK
No.
But some form of photo ID would be required by airlines and or ferry companies.
Passport
technically none but if travelling by air the airlines demand a passport
If you are an Irish or British citizen photographic ID will do, including a driving license. As a general rule, always use a passport for travelling.
If your travelling from the U.K. then you don't need a passport but some form of I.D. is reccommended. If your from Europe then you need a passport to get into Ireland. Outside of Europe then i think you need to apply for a visa and bring your passport.
Not if they're travelling from Northern Ireland, but from anywhere else he/she does.
No
No sorry
NoYou will need a passport or identification depending on your citizenship.
only if you are going to Northern Ireland, you need a passport to travel between England and Ireland.
The British passport is one that is recognized as used for the people of England.
No. They are both in Ireland, so if you are in Cork legally, then going to Dublin does not require any additional documentation. You may have needed a passport to get to Ireland in the first place. If so, then keep it with you when travelling around Ireland.
Generally you will need a passport to visit Ireland. As a general rule, you should always get a passport when travelling internationally. The fact that you grandmother is Irish, does not mean you can travel to Ireland without any passport. You may actually be entitled to get an Irish passport. See the related question below for details of documents needed to visit Ireland.