The best interview questions and activities are the ones where both you and the candidate can get a feel for what a person knows, how he/she works, and how well he/she will fit into your company. Questions should be relevant to the work they will be expected to do.
Random, oddball, "out-of-the-box" questions have very little correlation to the success a candidate will have on the job. They are most often used to satisfy the entertainment/curiosity of the interviewer, usually with the lame excuse that they are attempting to discern how the candidate thinks, views the world, handles "stress", etc. These are lame questions.
Consider my answers to the "killer" questions listed in the original question:
If The World Is A Stage What Role Would You Want To Play?
Director. Next question.
What Is Your Spirit Animal?
Human. Next question.
What would you do in the event of a zombie apocalypse?
Move out of the way (not my idea).
What might you infer from my responses? Virtually nothing, realistically. But you might be justified in thinking I could be pragmatic. What I'm actually saying (hidden by the starkness of printed words on a page), is that I'm not impressed by your questioning.
In my experience (I've been interviewing candidates off and on for 15 years), these types of questions most often come from inexperienced interviewers who were thrust into the role unexpectedly and scrambled on the Internet to find some questions to ask so they didn't feel/look stupid in front of a candidate. Over time, good interviewers find relevant questions and techniques and get good at evaluating the candidates' responses to them.