depends where your coming from, see the related link.
You don't need a passport to travel between the UK and the Republic of Ireland.
unfortunately you do
No
No they don't.
yes, because the republic of ireland is a seperate country from the UK you will need a passport to go there.
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.
In the UK, and also Europe since October 1998, children have needed their own passport and can no longer travel under their parents passports.In most other countries it is highly recommended that children have their own passports.If children are under the age of 18 they do not need a passport, for Ireland, however you will need their birth certificate. Anyone over the age of 18 will need a passport for Ireland.
As Belfast is in the United Kingdom and Dublin is in the Republic of Ireland, technically you may need a visa or passport to go there, depending on your nationality or other factors. However, there are no passport checks done on the train. Usually if you have been allowed access to Northern Ireland, you will also be allowed to get into the Republic of Ireland, but you need to check. See the website at the link below.
Yes they do need a passport for Northern Ireland
Children under 16 now need to have a passport, even babies. You can no longer put them on an adult's passport. Irish citizens are meant to be able to travel to Britain without passports, but in practical terms some form of identification is needed so people usually use their passport.
It is generally a good idea to have a passport when traveling. US citizens may enter the Dominican Republic without passports using other forms of ID and this is also true for children.