Is there a list with all the properties that I can set using the response after user authentication? like response.name, response.last_name and others? I would like to see a complete list.
Include line:
console.log(response);
in your javascript. Then download Firebug to your favorite modern browser and go to the console tab. You should be able to view the response as an object.
The complete response object for your case should look like this:
{ status: 'connected', authResponse: { access_token: '...', expiresIn:'...', signedRequest:'...', userID:'...' } }