I assume (but don't know!) that the "find people by entering their phone number" feature simply tries to find Facebook users with lax enough privacy settings such that (a) they expose their phone numbers to maybe friends or friends and (b) they allow non-friends to message them. Otherwise I feel like they would phrase it as "message people who aren't on Facebook!"

What Android screenshot are you looking at that makes you think it shows missed calls? I see two icons: a sort of bolt and a facebook "f". I think that the bolt means the user is using "Messenger" (i.e. fb on mobile) whereas the fb "f" means facebook.com.