What question(s) have no right answer?

I would suggest no, due to the fact that questions have answers, whether based on objective reality or subjective individuality. The right answer may not be correct or right for you but it would be right for someone, so ...

No, there is no such thing as a question with no right answer, unless of course you attempt to apply the answer to everyone, such as an answer like this one: "Rocky Road is the worst tasting ice cream on earth."

Seriously, ice cream rarely taste bad at all.