Jami,
If you would, start a new post for help with Authenticated Referrals. That's getting off topic, and this thread is getting pretty long already. If you've already setup anything regarding Authenticated Referrals, or need general information on where to start, let us know that in the new post as well so we know where to begin.
Regarding auto-login for mobile, that should work in most mobile browsers. However, not all browsers treat cookies the same, and some have much stricter restrictions on cookies and stuff like that in general. If the user is logged into a Facebook 'app', but not the website through a browser, that likely -not- automatically log the user in, as apps can't easily share information (Browers and FB app are different). If you run into issues with this though, or have other questions, again, please create a new post to keep things separate.
Finally, for posting in 'public', when you run Autotune, we have a record of your website URL, so you never need to make that public. Additionally, if you'd prefer, you can Private Message your questions as well by clicking the arrow under my picture (<
) and clicking the mail icon. PM's aren't always as fast, because I don't check them as often, and it's also directed to just me, instead of anyone else doing support, but it's a good way to keep things private if you'd prefer.
Hope that all helps!
Alex