They are not considered first cousins, unless your brother adopts them. If he did, they would be considered siblings and could not marry. Otherwise there is no legal relationship between them. They do not share a common ancestor.
Technically, if he does not adopt them, there is no legal relationship.
Your children are the first cousins of your brother's children, and the first cousins once removed of your brother's grandchildren.
They would be considered your 2nd cousins.
The children of your grandmother's brother (of your great uncle) are your parents first cousins and your first cousins, once removed. The grandchildren of your great uncle are your second cousins.
Your mother's sister's children are your 1st cousins.
The children of your great grandfather's brother are your grandparent's first cousins, and your first cousins twice removed.
The children of siblings are first cousins, so your daughter and your brother's daughter are first cousins to each other.
The children of your grandfather's brother are your first cousins, once removed. You can also call them by their names.
If you are referring to YOUR grandmother and grandfather then your children are their great grandchildren. If you are referring to your parents, then your children are their grandchildren. The primary kinship dominates.
They would be first cousins.
Your granddaughter and your first cousin's grandson are third cousins to each other. You find their common ancestor that is, your grand parents, and count the number of generations separating them, there are Brother and Sister then cousins, you and your cousin would be one (first cousins), your children and your cousins children are second cousins and their children are third cousins and so on.
Your brother or sister are your siblings. Your cousins are the children of your aunts and uncles.
Your half brother's children and your children are half cousins. However, in casual conversation, you can also refer to them as cousins, just as you can refer to your half brother as your brother.