I don't think that that's a requirement at all, unless you think that his second example question of a list of countries perfectly divides the population with not even a rounding error
If you don't evenly divide the remaining population of the earlier questions, you'll need more than 33 questions.
For the purposes of this problem (and most other purposes) if you have a question that divides answers in 47%:A 51%:B 2%:'stupid_question_doesn't_fit_me_I'll_answer_randomly', then it's still perfectly okay.
No, answering randomly is not okay. You will not be able to reproduce the bit string if there is a random answer any more than two source texts with a single bit changed between them will produce the same hash.