The granddaughter of your niece is your great great niece.
No.
If your great uncle married into your family some of his nieces and nephews are your aunts or uncles (or your parent) and some are not related to you at all.
great great (etc.) grandparents great grandparents grandparents + great uncles and great aunts parents + uncles and aunts [=parents' siblings] siblings + cousins [=uncles' and aunts' children] children + nephews and nieces [=siblings' children] grandchildren great gandchildren great great (etc.) grandhildren also cousins and second cousins [=(great-)grandparents' descendants]
great great (etc.) grandparents great grandparents grandparents + great uncles and great aunts parents + uncles and aunts [=parents' siblings] siblings + cousins [=uncles' and aunts' children] children + nephews and nieces [=siblings' children] grandchildren great gandchildren great great (etc.) grandhildren also cousins and second cousins [=(great-)grandparents' descendants]
When a couple is married and the wife has nieces who are daughters of her brothers or sisters, those nieces are also the nieces of her husband. So your great grandmother's sister's husband could have great nieces who are related to you and also great nieces who are not related to you.Note that your great grandmother's sister is your great great aunt.The great nieces who are related to you are the grandchildren of the siblings of your great great aunt.Those could be your:parentauntfirst cousins, once removedsecond cousins, once removed
Muslim men and women who are not closely related are not allowed to touch each other, even to shake hands. Close relatives include parents, children, grandparents, grandchildren, aunts, uncles, great-aunts, great-uncles, nephews, nieces, great-nephews, great-nieces, mothers-, fathers-, sons-, and daughters-in-law. Cousins and brothers- and sisters-in-law are not included in this class, as it is possible for Muslims to marry them.
The possessive form for the plural noun great aunts is great aunts'.Example: My three great aunts' house is a great place to visit.
Your niece's children are your great nieces and great nephews.
Your great nieces or newfews
Families in the Middle East are more traditional (fewer adopted kids, gay spouses, etc.) than Western families, but the members are the same: Mom, Dad, Brother, Sister, Uncles, Aunts, Grandparents, Great Uncles, Great Aunts, Nephew, Nieces, and a billion varieties of cousins.
There are Aunts, great aunts, great-great aunts, et al. A second aunt would be if you have two aunts and you prefer one over the other. But no there isn't.
They are your grand-nephews and grand-nieces or great-nephews and great-nieces.