I'm fond of #3. That said, if I'm asking someone to do a substantive amount of work, I should expect to compensate them for it.

I'd be leery of #5 were I being interviewed... the implicit task is really "Figure out what the interviewer thinks the right thing to do in this situation is, then give them a response that is close enough to that" rather than "Explain what the right thing to do in this situation is." If I cared a lot about interpersonal skills, I'd adopt approach #3 here as well: if what i want to confirm is that they can collaborate, or get information from someone, or convey information to someone, or whatever, then I would ask them to do that.

Q&A mostly tells me about their priorities. I'm fond of "What would you prefer a typical workday to consist of?" for this reason... there are lots of different "good" answers, and which one they pick tells me a lot about what they think is important.

I'm also fond of "Tell me about a time when you X" style questions... I find I get less bullshit when they focus on particular anecdotes.