I am new to LimeSurvey and I was wondering whether the software allows to track the time spent on each question/set of questions.

www.limesurvey.org/manual/Surveys_-_intr..._.26_data_management

Save timings: If enabled, the time spent on each page of the survey by each survey participant is recorded;

Like Jelo, but I just wanted to add something:
Take these numbers with a grain of salt, because what you are seeing is when the page has changed. So if you have more than one question per page (e.g. group by group modus), of course you can't tell how much time was spent per question, but only per group of questions.

And the second aspect: You only know how long they were on the page, not how long it took to respond. If they went to get a coffee in the mean time, you won't know.

But I guess you know this already, just wanted to highlight it again.

Thanks! I am interested in the time spent on a group of questions, so this feature is actually perfect for my goals. And my respondents will fill out the survey onsite, so I'll just make sure they are not getting any coffee in the meantime

Perfect, then you can control the situation a lot better and the data you are getting is a lot more meaningful.