Does Facebook's "find friend" algorithm get data from the iOS app? When I download a Facebook app on my smartphone (e.g. iPhone), what data does Facebook then access? Names? Telephone numbers?
Nothing is allowed until you poke holes in the app sandbox. iOS requires apps to request permission to access data outside their sandbox.

Open the settings app and look at privacy on iOS to see what your iOS and app have negotiated.

Most people expose far more data to Facebook by entering their credentials in the Internet Accounts section of the iOS settings app. Check there as well.