Yes, your passport.
Yes they do need a passport for Northern Ireland
If you are travelling from the USA to Northern Ireland, you need a passport to go there. You probably will also need a visa to enter Northern Ireland but you can find this out if you look up the British government website.
It should be fine as it is. As long as your initial marriage is legal, there shouldn't be any need to register it in Northern Ireland. It will be recognised.
No. Northern Ireland is part of the UK, so the visa will cover it.
It depends on where you are coming from As Northern Ireland is part of the UK you will need the same Visa that you would need to enter any other part of the UK. If you are a UK citizen you do not need one
No.
No! Don't be thick! And there isn't any need to write "the" before Northern Ireland.
They will need a visa to enter the United Kingdom in order to enter Northern Ireland.
only if you are going to Northern Ireland, you need a passport to travel between England and Ireland.
none if you are European. There are no border posts
No.No.No.No.No.No.No.No.No.No.No.
Northern Ireland as with the rest of the UK will accept sterling and/or Euro