Your son and your brother's grandchild are first cousins once removed.
That would be her great uncle I suppose. Common sense.
A person's grandchild and grand niece are 2nd cousins to each other.
They're related to you
Your daughter and your brother's child are first cousins to each other.Your daughter and your brother's granddaughter are first cousins, once removed, to each other. The "once removed" refers to the fact that they are separated by one generation if you count from their common ancestor, your parents.
Your mother gave birth to you, her child. When the child has a child that is a grand child. When the grand child has a child, that is a great grand child.
my great grand-daughter
Your child and your sister's daughter are first cousins. Your grand child and your sister's daughter are first cousins, once removed.
No. A great grand child is the child of your grandchild. The child of your grand niece is your grand niece or grand nephew, depending on the child's sex.
The relationship is that of a great great great grand uncle and great great great grand niece
There is no difference between a great nephew and a grand nephew. In some places "great nephew" is the preferred term for the grandson of one of your siblings. In other palces, grand nephew" is the preferred term for that relationship.
You are their Great Grand Nephew or Niece, which I think makes them your Great Grand Uncle. Ref: http://freepages.genealogy.rootsweb.ancestry.com/~gentutor/chart.html
Your grand-daughter's brother is your grandson. Their mother would be your child. Her mother-in-law is not related to you, as you do not share a common ancestor.