Yes, you will need to show your passport.
Strictly speaking, as the UK and France are both in the EU, you don't need a passport to travel to France. However, you will need a passport on your return to the UK. To be absolutely certain, you should check with the French Embassy.
A passport.
yes you need a visa
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.
Yes they do ! Just the same as British people need a Passport to travel outside the UK - so do Irish people !
A Nigerian national who is living in, but is not a citizen of Poland, and does not have a Polish passport, will need to apply for a visa to visit the UK.
It depends where you are coming from. A passport would be a very good idea though.
Assuming you are visiting Manchester in the UK you will not need a visa. Your United States passport allows you to stay in the UK for 90 days on the visa waiver programme. Hope this helps
You need a passport or an ID.
Yes, You always need a passport (or EU national identity card) to get in our out of the UK.
Visa required, except for a maximum stay of 6 months
No, unless one of your parents is a UK citizen and was one at the time of your birth. However, if you qualify for a UK Ancestry visa because one of your grandparents was born in the United Kingdom, then after living in the UK for 5 years, you can apply for UK citizenship + passport.