Your grandfather's great great niece is your second cousin, once removed
Your grandfather's sister is your great aunt.
For clarity, lets call your great great grandfather's niece "the niece". The relationship sequence: (1) The niece is the daughter of your great great grandfather's sibling (2) The niece is a 1st cousin of one of your great grandparents (3) The niece is a 1st cousin once removed of one of your grandparents (4) The niece is a 1st cousin twice removed of one of your parents (5) The niece is your 1st cousin three times removed
Your great great grandfather.
Most likely they would not be related to you
Your grandfather's niece is a first cousin of one of your parents. Her son is your second cousin.
Your great great niece is the granddaughter of your niece or nephew. Your daughter and your niece or nephew are first cousins. Your daughter and your great great niece are first cousins, twice removed.
Your husband is great uncle to your niece's son (your great nephew).
Your aunt's grandchildren would be your first cousins once removed, as the your aunt's children are your first cousins.
great nephew
Great-niece.
You are the great-great-aunt/uncle to your niece's granddaughter. This means that your niece's granddaughter is your great-great-niece. The term "great-great" signifies that there are two generations between you and your niece's granddaughter.
There probably isn't a relationship. You do not share a common ancestor.