Northern Ireland was not established and did not exist as a country when the Liberals felt that Home Rule should be implemented. It would bring about a self government for all of Ireland. There were four Home Rule bills drafted from 1886 to 1920, the latter being named the Government of Ireland Act. The GoA established two Home Rule entities, one being Northern Ireland and the rest of Ireland. The rest of Ireland did not accept this as since the Easter Rising of 1916 it became clear that Sinn Fein and others' interest in Home Rule had faded and they were now seeking complete partition from the Britain.
The term goes back to when Ireland was still completely under British rule and did not have a parliament of its own, between 1801 and 1921. Home Rule was the desire by some for Ireland to have its independence and rule itself. The term is not really used now, but it would now be the concept of a united Ireland. Currently Northern Ireland is part of the United Kingdom.
Home Rule in Ireland was the demand to cancel the Act Of Union of 1800 and confer a degree of Independence on Ireland.
Ireland was under British rule up to 1922. Northern Ireland was created at that time, and it is still under British Rule, while what is now called the Republic of Ireland is independent.
England
No. The UK consists of Great Britain and Northern Ireland. In many respects Northern Ireland has its own government.
The Republic of Ireland uses the Euro. Northern Ireland uses Sterling. It is because Northern Ireland is under British rule and so it uses the British currency.
Ireland
The Home Rule
Up until 91 years ago all of Ireland was ruled by Britain and wanted freedom from UK rule, (With the exception of Protestant groups in Northern Ireland) The south obtained freedom but Northern Ireland has not - there are still some groups in Northern Ireland that want freedom from the UK
They feared being a minority in a country dominated by Catholics. ( In 1994, parliament enacted a home rule bill for southern Ireland )
Ireland is independent, so it is not ruled by any other country. Northern Ireland, which is different to Ireland and may be what you are referring to, is part of the United Kingdom.
England, Ireland, Northern Ireland, Scotland, Wales, Australia, Bermuda, British Virgin Islands, New Zealand, Gibraltar, The Philippines,