The grandchild of your great grandmother's sister is your second cousin, once removed.
If your great great grandmothers were sisters, your common ancestors are your great great great grandparents. That makes you 4th cousins.
Your grandmother's sisters are your Great Aunts.
Yes, along with your grandfathers' sisters, if any.
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.
It would technically be considered your half- cousin since you do have the same grandmother but a different grandfather.
You and your uncle's great grandchild are first cousin, twice removed.
Your sister would be her great aunt and she would be your sisters great niece.
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If the daughter is biologically related to you, it would be your great-grandchild. If your husband had his daughter before he married you (which would make her your step-daughter), it would be your step-great-grandchild.
The grandchildren would be the parents, aunts and uncles, and first cousins once removed, of the great grandchildren.
Your grandmother's sister is your great aunt. Her son's child is her grandchild. You and your great aunt's grandchild are second cousins.
You are great great aunt to your niece's grandchild. Your children and your niece's grandchild are first cousins, twice removed.