A paternal niece is a niece on the fathers side. For example:
my dad's sisters's daughter is my paternal niece
Your grandmother's brother is your great uncle and you are his great niece or great nephew. Your child is his great great niece or great great nephew.
If you are a boy, you are a nephew to your uncle. If you are a girl, you are a niece. The English language makes no distinction between relationships with a paternal or maternal relative. Uncles are uncles, nephews are nephews, etc., regardless of which side of the family they may be on.
Your mother's uncle, whether maternal or paternal, is your great uncle. You are his great nephew if you are male, and his great niece if you are female.
Since it's her husband's niece the niece is just your sister's niece through marriage and not your niece.
The noun form for the adjective paternal is paternity.
"Paternal" means "on your father's side". Your paternal great-grandfather would be one of your father's grandfathers.
The grandparents on the father's side of the family
Your mother's niece is your first cousin. Your first cousin's daughter is your first cousin, once removed.
Your niece's daughter is your grand niece, or, as some would say, your great niece.
Your niece's child is your great niece if she is a girl, or your great nephew if he is a boy.
No. Your wife's niece is also your niece, but the husband of the niece is not related to you or to your wife.
Your sister's daughter is your niece. If you are a woman, you are your niece's aunt; if you are a man, you are your niece's uncle. Your sister's son is your nephew.