If your brother (or your sister) has children they are your nephews (males) and nieces (females).
Your children are the first cousins of your brother's children, and the first cousins once removed of your brother's grandchildren.
Your sister's husband is your brother-in-law. Your brother-in-law's brother is not related to you and neither are his children. But he is your sister's brother-in-law and his children are your sister's nieces and nephews.
Assuming the brother who died with a will was unmarried and had no children, and assuming his beneficiary brother predeceased him, his estate would pass to the children of his siblings. If he had only one brother then his brother's children would inherit his estate.
Your brother's children would be your nieces and nephews.
Your brother-in-law's children are your nephews and nieces.
An Uncle
Your brother's children would be your nieces and nephews. Your nephew's children would be great-nieces and great-nephews.
Your dad's brother is your mom's brother-in-law. He is not related to your mom's sister or her children.
No he doesn't have children
Great Aunt/Uncle
Your brother-in-law. He would also be the uncle of your children.
The children of your grandfather's brother are your first cousins, once removed. You can also call them by their names.