I have a few last doubts. Thank yo very much for your corrections.

1)The narrator can tell a story using a first- or a third-person.
An internal narrator tells of his own personality. (or tells about?)
2) The story deals with (and not tells about) a family living in New York.
The story tells of a family?

1. The narrator can tell a story using either first- or third-person point of view. An internal narrator usually tells about his own personality.

2. The story tells about a family living in New York. (Do you mean New York City? or somewhere in the state of New York?)