What is a motif?
a. a repeated element
b. something that is used to stand for something else
c. the main idea
d. a message or main idea

c. the main idea

A motif is a theme that reoccurs and has symbolic significance in a story. This helps the reader understand the plot.
The plot of a story is the storyline or the order in which events take place. 

A theme is the idea of the message of the story. The message of the story is spread via the plot and the motifs. 

The author's purpose in writing is his/her reasons for writing the story. There can be no exact interpretation of the author's purpose in writing the story. However, the purpose of the author in writing a story can be summarized into three using the acronym PIE. P stands for persuade, I for inform and E for entertain.  These are the three possible purposes for the author in writing a story. To persuade or convince is the main type of the author's purpose in writing.