I'm afraid I don't quite understand the point of the second question. Does the answer mean to state authoritatively that that engineers are no more likely to do carpentry and partake in recreational mathematics than lawyers, or is there another explanation? If it were changed to something like "2. A team of psychologists performed personality tests on 100 professionals, of which 50 were engineers and 50 were nurses.…
With this in mind:
The point we're supposed to accept is that when asked to evaluate the data sets presented, one heuristically makes assumptions based on social norms and crystallised intelligence. I'm pretty sure that this hypothesis was made in the article preceding the quiz, so no excuses for not realising the point of, well, any of the questions.
For the theatre question, I too started with your interpretation. However, it didn't make sense in the context of illustrating the author's hypothesis, so it couldn't have been the "right" answer.
Protip: when considering someone's line of argument in anything but a hard engineering discipline, I usually play the man before the ball - it's much more revealing.