Your first cousin's grandchild is your first cousin, twice removed.
Your brother's grandchild is your Great Nephew or Great Niece and you are their Great Aunt or Great Uncle.
Your children are the first cousins of your brother's children, and the first cousins once removed of your brother's grandchildren.
Yes, they are related. While it is a distant relationship, you are cousins.
Your sister's great grandson is your great great nephew. You are his great great uncle, or great great aunt.
They would be second cousins, once removed. The descent is from a common ancestor. Thus 1st cousins share a grandparent as a common ancestor. 2nd cousins share a great-grandparent as an ancestor. If the descent from the common ancestor is not an equal number of generations, the inequality is expressed as 'removed' from the oldest generation being compared.
Your grandchild and your niece are first cousins, once removed.
The grandchildren would be the parents, aunts and uncles, and first cousins once removed, of the great grandchildren.
You and your uncle's child are first cousins to each other. You and your uncle's grandchild are first cousins, once removed, to each other.
You would be Second Cousins
Your child and your sister's children are first cousins. Your grandchild and your sister's children are first cousins once removed.
Your child and your sister's child share a common grandparent and are first cousins. Your grandchild and your sister's grandchild share a common great grandparent and are second cousins. There is a generation out of synch, so they would be second cousins once removed.
The grandchild of your grandmother's first cousin is your third cousin. The grandchild of your grandmother's second cousin is your fourth cousin. The grandchild of your grandmother's third cousin is your fifth cousin.
You and your first cousin's grandson are first cousins, twice removed, to each other.
You are great great aunt to your niece's grandchild. Your children and your niece's grandchild are first cousins, twice removed.
Your First Cousin and your children are related as First Cousins once removed.
Yes, of course your son and your great niece are related. They are first cousins, once removed, to each other. (Your great niece's parent, your niece or nephew, and your son are first cousins to each other.)
You are the grandchild of your grandfather. If that grandfather had children other than your parent, and that child had a child - that person is your first cousin and also a grandchild of your grandfather. Your first cousins are, by definition, all those who are not your siblings but are also grandchildren of one of your grandparents. Remember that you have two sets of grandparents. Those first cousins who are related to you through one pair of grandparents are not related to your other grandparents at all.