Your grandfather's first cousin's niece could be:
Yes. The granddaughter of your grandfather's first cousin is your third cousin, and you are her third cousin.
Your grandfathers' sisters' grandchildren are your second cousins.
You would be second cousins.
Some of your granddaughter's first cousins are also your grandchildren, others are not related to you at all.
You are second cousins
She would be your aunt. The neice's kids will be your second cousins.
They would be the fourth cousins. They share a common 5 Great Grandparent.
First cousins three times removed.
Most likely they would not be related to you
yes
Your granddaughter and your first cousin's grandson are third cousins to each other. You find their common ancestor that is, your grand parents, and count the number of generations separating them, there are Brother and Sister then cousins, you and your cousin would be one (first cousins), your children and your cousins children are second cousins and their children are third cousins and so on.
Your daughter's daughter is your grand daughter. Your nephew's daughter is the granddaughter of your sibling (your brother or sister) The grandchildren of siblings are second cousins.
Your granddaughter and your grandniece are second cousins or third cousins to each other