Hey BTW, you can watch Stalker officially for free on Youtube, here's the URL:
   • Stalker | FULL MOVIE | Directed by An...  

Give it a shot!

Chapter information:

00:00-00:30 - Intro
00:30-01:20 - Explaining Basics
01:20-02:45 - Exploring Zone
02:45-04:48 - The Meat grinder
04:48-06:00 - The Danger
06:00-08:00 - The Characters
08:00-09:00 - Happiness?
09:00-10:45 - Different Views
10:45-12:45 - The Myth
12:50-13:50 - SPOILER!



--SPOILERS BELOW--
About the question of wether it's real or not for Tarkovsky...
I think it is real for him. As I mentioned he was religious, meaning that he believes in the room within the context of this video.

As to the proof, I think there's couple, but the most important is this:
At the end of the movie Stalkers child telepathically moves the glass on the table in the real world. Thus confirming that something extraordinary is truly happening in this world.