Data sets of questions asked in conferences
Such a data set probably does not exist, due to human subjects considerations.  While conference speakers are often asked to consent to possible recording of their talks, conference attendees are not generally asked for such consent.  Sometimes questioners do get recorded anyway, in those rare talks that actually are recorded, but they have certainly not provided any explicit consent for becoming experimental subjects.  

Now, some researcher and their IRB might well be able to work out a way to build a data set from the decidedly biased sample of publicly available talks that happen to include questions. Doing so and then executing that project, however, is likely to be a rather large research and coding effort and with that much work the authors would certainly end up wanting to publish papers on it.

In short: if your literature search isn't turning it up already, then it doesn't exist.