Your father's aunt's daughter is your father's first cousin and your first cousin, once removed.
They'd be your cousin.
First cousins, twice removed. Aunts daughter is your cousin. Aunts daughters daughter is cousin once removed Aunts daughters daughters daughter is cousin twice removed.
Your father's brother's son is your first cousin and your daughter's second cousin.
the daughter's cousin
yes
Your first cousin.
Your uncle/aunt's son/daughter is an adult and you are still small, your uncle/aunt's daughter had a child, and that child will call you uncle. Uncles/aunts are your dad/mom's siblings.
Her aunts/uncles daughter.
great nephew
The grandchildren of any of your great uncles and great aunts are your second cousins.
your second cousin
your 5th cousin