Real sister, half sister, or step sister
The sister's son would be the nephew of her brother.
No. The sister is a relation, and her husband is an in-law. The husband's brother is no biological relation either. Therefore, the great granddaughter of the husband's brother is not a relation.
No relation
Your brother's wife is called your "sister-in-law." If you are a male, you are her brother-in-law and if you are female, you are her sister-in-law.
If your sister-in-law is the sister of your spouse, her brother is your brother-in-law (or your husband if you are a woman).If your sister-in-law is the wife of your brother, then her brother is not related to you.
If your sister marries someone else's brother, that brother is your brother-in-law (and you are his brother-in-law or sister-in-law), but you are not related to that someone else.
If your brother-in-law is your spouse's brother, then his sister's daughter is your spouse's niece, and your niece, too. If your brother-in-law is your sister's husband, then his sister is not related to you, and neither is her daughter.
Great niece
Your husband's brother's wife or your husband's sister's husband have no relation to you. Your brother's or sister's wife or husband is called a sister or brother in-law. You are only related by the marriage between them and your sibling.
No relation whatsoever. You will be an aunt or uncle to your sister's child and your brother-in-law's sister will be the child's aunt, but that's as close as it gets.
Your dad's brother is your mom's brother-in-law. He is not related to your mom's sister or her children.