You can only read the user wall with an active user access token, and the read_stream permission.
About the insights: maybe with this graph connection?
/[post-id]/insights
Well, it gives me nothing for a valid post id. But i am sure you can only get the insights of pages, not user accounts. See here (about pages, but maybe useful additional info): Unable to access a post's insights for someone else's page
One more reason why it will not work, just popped up in my head: If you go to a facebook page, you have the insights view as admin. Nothing like that on a user profile. So the only thing you can track is how often a link to your app has been clicked after posting it to a user profile. You can easily add tracking information to the link too, so you always know from which profile the click comes.