Your niece would be your mothers granddaughter.
You and your mother's niece are first cousins to each other, so your and the niece's daughter are fist cousins, once removed.
Aunt or uncle and they nephew and niece, there's not other relationship term that can fit that relationship unless in a mother tongue.
Your wife's niece is also your niece, and her daughter is your great niece. It is to be hoped that you do not have a relationship WITH her, merely TO her.
Your great uncle's niece could be your mother, or your aunt. It is also possible that she is not related to you at all, as you might not share a common ancestor.
There is no actual blood relationship. If this was your mother's niece, it would be your first cousin. In most families, she would be referred to as a cousin, even without the blood connection.
great niece
Great grand niece
Assuming that you are a female and that your mother actually has a brother, then yes, you are your mother's brother's niece.
Your niece's child is your great niece if she is a girl, or your great nephew if he is a boy.
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.
You and your father's niece are first cousins.