Your first cousin's daughter and you are first cousins, once removed. Your first cousin's children and your children will be second cousins to each other.
You are one generation out of synch. That would make you first cousins once removed.
Your nephew and your daughter are first cousins to each other. Your nephew's son and your daughter are first cousins, once removed. Your nephew's son and your daughter's child would be second cousins to each other.
I think the kids would be second cousins
Your daughter and your first cousin are first cousins, once removed, to each other. Your daughter and your second cousin are second cousins, once removed, to each other.
Your daughter and your sister's son are first cousins to each other. Your sister's son's daughter (her granddaughter) and your daughter are first cousins, once removed.
I think the kids would be second cousins
You are out of synch with the common ancestor by 2 generations. It would be first cousins twice removed.
Your half-brother's daughter is your niece. Your niece and your son are first cousins to each other.
You are one generation out of synch. That would make you first cousins once removed.
Your cousin's daughter is your first cousin once removed. Your daughter and your cousin's daughter would be second cousins.
That would be second cousin once removed. Your parent and your grandmother's sisters daughter were first cousins. You and the daughter's daughter are second cousins. There is a difference on one generation between the two of you.
Your niece and your son or daughter are first cousins. That would make your niece and your grandchild first cousins once removed. Your niece's child and your grandchild are second cousins.