If your great great great great great grandfather was from Ireland and none of your ancestors in other lines were Irish, then you would be said to be 1/128th Irish. But no one bothers with such small fractions.
The sister of your great great great great grandfather is your great great great great great aunt. Her great great grandchild is the fourth cousin of your grandparent and your fourth cousin, twice...
That depends upon which family line you wish to follow. Like everyone else, Prince William has two grandfathers, four great-grandfathers, eight great-grandfathers... and so on. If you follow his...
The great great great granddaughter of your great grandfather could have any of the following relationships to you. She could be your: granddaughter great niece first cousin, twice removed second...