What relationship is your nan's cousin's daughter to you?

Answer 1

To keep it simple, let's call your great grandmother's niece "The niece"

The sequence of the relationship:

(1) The niece is the daughter of your great grandmother's sibling

(2) The niece's sister is also the daughter of your great grandmother's sibling, and therefore also her niece.

(2) The niece and her siser are 1st cousins of one of your grandparents

(3) The niece and her sister are 1st cousins, once removed, of one of your parents

(4) The niece and her sister are your 1st cousins, twice removed

Answer 2

Your grandmother's cousin's niece is your parent's second cousin and your second cousin, once removed.

Answer 3

If by Nan you are referring to your grandmother, you and her first cousin's daughter are second cousins once removed. The first cousin's daughter is a second cousin to one of your parents.