Site-wide variables not available in controller/model files

1) Is it good practice to pass data around using $_SESSION? I don't really like it, I would rather have them loaded from file like it happens in the non-admin (non-CI) area of the website

No.

2) Is it good practice to add those lines to 'index.php' file?

No, and that wouldn't work anyway - they'd be outside of the controller's scope.

3) Is it good practice to start the session this way (and in that location, again index.php)?

No.

4) Is the controller code above the right way to go?

No, and you don't need that 'php_session' thing at all.

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Easiest way is to use constants, because they aren't affected by scope visibility.

Thanks for your answer, but I have to say I was hoping for more info on how to achieve the desired effect, and why it is not good practice, not just that it is not.

session_start() in index.php works, from what I can see, and all the code I pasted above works.
Why do you say it won't work? 

Why don't I need 'php_session' ? How can I can the session variables without using php_session?

About defining constants: there would be a lot of them and not sure that would be good practice wither, I never seen this approach in any code I inspected. 

If you can elaborate a bit on your answers, why I should not put session_start in index.php, where should I put it (I definetely need the session started at some point, as the login took place already so the user data is in the session), how can I get session data without php_session etc I would really appreaciate it. 
I tried searching and googleing on this issue and some were recommending the Session approach, which you say it is not a good idea. Confused now... However, so far, the code above is working fine in production.