Where can I see the data Facebook knows/has about me, a person who has not registered for the service?
I've never signed up for Facebook. I tried back in 2006, but was denied, and never finished the registration process. Since then, I've never tried to log in to it. Of course, 99% of my friends have Facebook, and I don't even know what information my friends have on me!
Almost every app nowadays also "integrates" with Facebook, to an extreme! I always root my Android phones and remove the built-in Facebook app as soon as I get a new phone. I never let people sign into Facebook on my phone, whether it be through the website or the app for the couple weeks I ignored it being installed.
I read a question on Information Security about how Facebook could know recommendations of friends by just a phone number. So further to that there must be a place or page where one can see the stored data Facebook has against them.
Best Answer
The answer to that question explicitly details that the more probable scenario is one in which the friends of the phone contact shared the information to Facebook.
So let's start there. Let's assume a phone number is in a contact list "123-4567"
At this point, before a friend syncs to Facebook. All this is a number, not a name, not an address.
You can state here that Facebook holds phone numbers (because Facebook users allow them to) to assist with the Suggested Friends / People you may know feature.
With you interacting with Facebook in anyway
https://www.facebook.com/legal/terms
In terms of the registration specifically, since you never finished the process then the user you registered isn't validated. Why would Facebook store dirty data since 2006?
With actual requests of data use this form
https://www.facebook.com/help/contact/166828260073047