Your sisters grandson would be your grandnephew.
Your brothers great granddaughter is your great great niece.
You would be 2nd cousins, assuming that the brother's wife's granddaughter is also the brother's granddaughter. If the granddaughter is not the granddaughter of the brother, there is no relationship.
Your sister is her great grandaunt.
Your granddaughter is your sister's great niece. Your sister is your granddaughter's great aunt.
They are brothers.
Your granddaughter and your niece's son are second cousins.
Your granddaughter could be your son's daughter, or your son's niece.
If you really need a relationship term, use granddaughter-in-law. Most people would merely say "my grandson's wife."
Grandniece
Your granddaughter and your sister's grandson are second cousins.
Close family friend
Your brother's daughter is your niece and his granddaughter is your great niece.