You mother's first cousin is your first cousin, once removed.
Your mother's aunt's son is her first cousin and your first cousin, once removed.
The relationship between your sister's (or brother's) child and your cousin is the same as the relationship between your child and your cousin. Your child and your first cousin are first cousins, once removed. Your child and your second cousin are second cousins, once removed, and so forth.
First cousin, once removed.
First Cousin, twice removed.
The offspring of your first cousin is your first cousin once removed.
The child of your first cousin, once removed, is your first cousin, twice removed, or is your second cousin, depending.
She is your first cousin.
If your uncle's cousin is also the cousin of your parents, you are first cousins once removed. If not, there is no relationship as you do not share a common ancestor.
First cousins once removed.
Your nephew and your first cousin are first cousins, once removed, to each other.
The children of your wife's first cousin are her first cousins, once removed. They are not related to you.
Your daughter is first cousin once removed to your cousin. Your daughter is second cousin to your cousin's children. Your cousin's children are first cousins once removed to you