cousin daughter
A niece. How could you not know that
Your father's niece is your first cousin. Her son is your first cousin, once removed.
Your father's niece is your first cousin. Her son is your first cousin, once removed.
Your cousin's niece.
Your mother's niece is your first cousin. Your first cousin's daughter is your first cousin, once removed.
You are either her aunt or uncle depending upon your gender, and she is your niece.
niece in-law
For clarity, lets call your great great grandfather's niece "the niece". The relationship sequence: (1) The niece is the daughter of your great great grandfather's sibling (2) The niece is a 1st cousin of one of your great grandparents (3) The niece is a 1st cousin once removed of one of your grandparents (4) The niece is a 1st cousin twice removed of one of your parents (5) The niece is your 1st cousin three times removed
For clarity, lets call your great great grandfather's niece "the niece". The relationship sequence: (1) The niece is the daughter of your great great grandfather's sibling (2) The niece is a 1st cousin of one of your great grandparents (3) The niece is a 1st cousin once removed of one of your grandparents (4) The niece is a 1st cousin twice removed of one of your parents (5) The niece is your 1st cousin three times removed
to you, she is your first cousin. to your father, she is his niece.
It will depend on whether you share a common ancestor (is the niece's parent also a cousin?). If you do not, you are technically not related. If you do (you both have the same grandparents) you would be second cousins.
Your cousin is your Uncle/Aunt's son/daughter. Your niece is your brother/sister's daughter. So your parent's niece is your cousin.