Why would Kubrick put all these hints in the movie and which ones are true?

I think some may be valid but some are just there so the public could chase their collective tails trying to understand them. Kubrick knew there was an audience who loved to analyze his films to death. So why not have a little fun with them? The Beatles did this with some of their music. People were analyzing their songs to death. So John Lennon filled songs like "I am the Walus" with a bunch of no-nonsense clues just to have some fun.