Not appropriate questions but probably no more useless than some of the things I've been asked (or, occasionally, not asked) in job interviews.
I once went for an interview with a firm that had a Government contract to assist the long-term unemployed back into work. As, at that time, I was one of the long-term unemployed myself (and also had a cv which matched up very well with the job requirements) I thought that I might stand a reasonable chance of become one of their counsellors.
I was there for nearly two hours but the guy who was 'interviewing' me didn't really ask me anything. All he keep doing, over and over again, was going on about how (if I got the job) my task would include ensuring that the people we were trying to help got 'prompt and meaningful feedback' from any interviews which they attended. After he'd told me that over a dozen times, I started to keep count of how many times he said it again and the count got to well over 50.
When I left I wasn't sure of whether I'd got the job or not but (after being told over 60 times how important 'prompt and meaningful feedback' was to the company) I expected a swift and useful reply.
What I actually got was a one-sentence letter, telling me that I hadn't got the job, which was hardly 'meaningful feedback'. It wasn't particularly prompt either, as they sent it to me ten months after my interview!