Kevin o'brien(cricketer) belongs to Republic of Ireland or Northen ireland ?

What is the capital city of both the nations ? I am confused as Northen ireland is the part of UK & UK consisting of four countries: England, Northern Ireland, Scotland, and Wales and has the capital london(as per wikipedia) it also refers Belfast, Cardiff and Edinburgh, the capitals of Northern Ireland, Wales and Scotland respectively. Do all these countries have independent parliamentary system and have their own government and individual constitution and administration without having any influence of Britain ? ....I may be mistaken somewhere i apologies for that...i will be obliged if anyone can enlight on my confusion.