A story about the life of an author, written by the author, is a

biography

Explanation:

an account of someone's life written by someone else.

i have heard the mermaids singing, each to each.

i do not think they will sing to me

one thousand and one nights, also known as arabian nights is a collection of stories whose basic structure is that of embedded narrative. this technique refers to a main story which works as the common frame - or framing narrative - for the other stories, and then this series of stories which are connected to the main one. this technique can also be referred to as a story within a story. the stories stem from the original tale, some begin and end on their own, some are connected to the previous or following one, by means of questions that are answered in the subsequent tale, or characters which reappear.