Unless you are a citizen of a country that has a visa-free arrangement with Ireland, you cannot enter the country without one.
Ireland
Yes.
No. Limerick is not in Britain, so a British visa has no relevance there. Limerick is in Ireland. You may need a visa to go to Ireland. That will depend on things like where you are from and Ireland's visa arrangements with that country.
They will need a visa to enter the United Kingdom in order to enter Northern Ireland.
Yes, you need a separate visa for Ireland. Ireland is not part of the Schengen Area. Schengen visas are not valid.
yes there are no borders between northern and southern ireland
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
If you are a Spanish National or a citizen of another European country then you do not need a visa to travel to Ireland. Anyone who holds a passport and is a citizen of the European Union is free to travel anywhere within the union.
Yes
Ireland is not part of the Schengen Area so Schengen visas are not valid in Ireland (or the UK). You may need a visa unless you hold a passport from a country which doesn't need a visa for Ireland (e.g. USA). Check the Irish embassy for your country to see their rules.
Fijian citizens can visit Ireland visa-free for 3 months.
It can depend on where you come from. Different countries have different arrangements. However, generally the visa system used for Ireland does not entitle you to go to Britain. A separate visa would be required.