Your granddaughter and grand niece are second cousins to each other.
You are the great-great-aunt/uncle to your niece's granddaughter. This means that your niece's granddaughter is your great-great-niece. The term "great-great" signifies that there are two generations between you and your niece's granddaughter.
Your brothers granddaughter is your grandniece.
your niece
Your sister's grand daughter is your grand niece or great niece. You are her great aunt or great uncle.
Your granddaughter is your brother's grand niece (or some would say, great niece).
Your granddaughter is your brother's grand niece (or some would say, great niece).
Great niece
Your grand-niece.
Yes
Your sister's son's daughter is your sister's granddaughter and your great niece. (Some would say "grand niece.") You are her great uncle or great aunt.
You granddaughter is a great great niece of your aunt. Your aunt is your granddaughter's great great aunt.
Your sister's daughter is your niece. Your sister's granddaughter is your great niece Your sister's granddaughter's daughter (your sister's great granddaughter) is your great great niece. You are her great great aunt, if you are a woman, or her great great uncle, if you are a man.