Great niece's baby is your great-great niece or great-great nephew.
The system works like this:
Second cousin.
She is a first cousin twice removed.
grandniece
Your niece's child is your great niece if she is a girl, or your great nephew if he is a boy.
They are first cousins once removed.
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.
If you are male, you are great uncle to your niece's child. If you are female you are great aunt. The child is your great nephew (if it is a boy) or great niece (if it is a girl).
The great aunt is the great niece's baby's great-great aunt.
That is difficult to say. Their niece could be your daughter. They could be your niece as well if they are the child of one of your siblings. Or there could be no relationship at all if there is no common ancestor.
they would be cousins.
Say a woman (let's call her Jane) has a daughter (let's call her Mary) and the daughter (Mary) has a child (let's call the child Carol) Jane is the grandmother of Carol. If Jane has a child other than Mary, that child is Carol's Aunt or Uncle and Carol is that child's Nephew (if Carol is a boy) or Niece (if Carol is a girl). So the relationship between a grandmother's baby and her daughter's baby is that of Aunt/Uncle to Niece/Nephew.
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.
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.
A person's grandchild and grand niece are 2nd cousins to each other.
Your sister's child is your nephew if it is a boy, or your niece if it is a girl.