The child of your niece is your great nephew (if the child is a boy) or your great niece( if the child is a girl). You are the child's great aunt, because you are a woman. A man would be the child's great uncle.
The child of your niece is your great niece or great nephew. You are that child's great aunt (or, some would say, grand aunt.
Your daughter and your niece are first cousins. Your daughter's child and your niece's child are second cousins.
The son would be a first cousin once removed to his mother's aunt's children
The niece and her aunt's children are first cousins.
I believe that is called incest. I don't think that is legally allowed. The child will be prone to deformities as well because it is such a close relationship of inbreeding.
She would be his grand niece. He would be her great uncle.
Your uncle is your child's great uncle. Your child is his great niece (if a girl) or great nephew (if a boy).
You are the great uncle of your niece's child if you are male. If you are female, you are the child's great aunt.
great niece
You are your uncle's niece. You and your uncle's children are first cousins to each other.
You are her great-aunt/uncle. She is your great-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.
A niece or nephew is the child of an aunt's or uncle's brother or sister. So the parents of the aunt/uncle and of the niece's/nephew's parents are the same people - their grandparents. The grandmother of the aunt or uncle is the great grandparent of the niece or nephew.
Great great aunt/uncle. To your niece, you are the aunt/uncle, to her child you would be the great aunt/uncle. So you would then be the great great aunt/uncle of her child's child (her grandson)
Your niece's child is your great niece if she is a girl, or your great nephew if he is a boy.
You are the great aunt/uncle
Uncle and niece.
You are their great-uncle/aunt.