Should I include extra information in quiz questions?
It is always a good idea to offer authentic questions or tasks for assessment. So, if this additional information is authentic part of the problem, it is good to include it.  For example, if you would put it in the Introduction section of your paper on the topic of the quiz, you can include it in the quiz.

However, from the reading point of view it makes it harder to process, particularly for language learners. Any unnecessary bits should be left out.

Ideally, you should find the right balance between these two contradictory factors.