Your great great grandmother's niece is the daughter of her brother or sibling and thus the first cousin of one of your great grandparents. Therefore, the niece is your first cousin, three times removed
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 grandfather's great great niece is your second cousin, once removed
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).
If you are a woman, you are great great aunt to your niece's granddaughter. If you are a man, you are great great uncle to your niece's granddaughter. In either case, your niece's granddaughter is your great great niece.
great nephew
Great-niece.
You are your neice's aunt, your neice's children's great aunt, and your neice's grandchildren's great great aunt
There probably isn't a relationship. You do not share a common ancestor.
Your brother's daughter is your niece. Her daughter is your great niece.
Your niece's son's daughter is your great grand niece. Your niece's son is your grand nephew or your great nephew, whichever term you prefer.
Great niece