Yes, her use of "double" is the same.
http://www.studyguide.org/lit_terms.htm
We just don't get enough of the narrator to see if there is a part of him that is like Ethan. At least I don't think so.
Well, the very first sentence of the novel is, "I had the story, bit by bit, from various people, and, as generally happens in such cases, each time it was a different story." Do you think Wharton is saying that she does not get part of the story from Ethan? If not, how could she know his internal feelings?