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.
You would need to get at least 2 trains, one from Belfast to Dublin and one from Dublin to Cork. They are at different stations, so you would have to travel from one to the other on arriving in Dublin, which you can also do by rail. The whole journey from Belfast to Cork could take between 5 and 6 hours, depending on the times you travel and the connections for the departure times.
does my passport need to be in date to go to belfast
No
No, Belfast is in Northern Ireland which is part of the UK - you don't need a passport to travel from one part of the country to another.
technically, yes, unless you are a citizen of Ireland or the United Kingdom Very often people are not asked for passports but you should have one if you are a citizen of any other country
No
no, as long as you have a passport
No but you do need I.D.
Yes
If you are talking about Euston Station in London, to Dublin port, then it would be an international journey so you may need a passport. It will depend on your nationality. If you are talking about Heuston Station in Dublin to Dublin port, then it is a journey within Ireland, so that journey itself would not require a passport, but you may have needed one to get into Ireland in the first place.
no you dont
You need a passport to enter any country, that's why you have passport control at airports.