No. A great grand child is the child of your grandchild. The child of your grand niece is your grand niece or grand nephew, depending on the child's sex.
Your niece's child is your grand-niece or grand-nephew, and they would be a cousin to your children.
Your niece's son is your grand-nephew. You are the child's grand aunt, or grand uncle (whichever applies).
A person's grandchild and grand niece are 2nd cousins to each other.
Your brother's or sister's son is your nephew. Your nephew's or niece's child is your grand-nephew or grand-niece.
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.
Your grand niece and your grand child share a common great grandparent. There is no generation difference. That would make them second cousins.
you would be the child's great aunty or uncle Therefore, they would be your great niece or nephew.
Yes, your niece's daughter is your grand niece. You are her great aunt or great uncle.
Your niece's son is your grand-nephew. You are the child's grand aunt, or grand uncle (whichever applies).
Great nephew. Your children are the first cousins of your niece and your children would be first cousins once removed. Your grandchildren and your niece's child would be second cousins.
Your mother's brother is your uncle. Your uncle's daughter is your first cousin. Any child of your first cousin is your first cousin, once removed.