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.
Your Mother would be your Neice's "Great Aunty"
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.
Assuming that you are a female and that your mother actually has a brother, then yes, you are your mother's brother's niece.
Great grand niece
great 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.
Your niece's grandson is are your great-grandnephew.