One of my students would like to figure out how long a person took to do a survey. Is it possible to somehow store how long each question took (as a difference between timestamps, not as a timestamp, so that anonymity can be preserved).

Yes, I am aware you can put time limits on some question types (long free text), but not on others (numerical input), but that's not the same thing as what this student would like.

Actually, you can only have start date and end date.

You can add this functionnality to our feature request : ideas.limesurvey.org/