I would like to split question into two parts:
1) Ubhaya Bharati was appointed the judge between Adi Shankaracharya and Mandana Mishra. After Mandana accepts defeat from Shankaracharya, why was Ubhaya Bharati allowed to ask question? Example: An umpire in a cricket game cannot play the winner of two opponents. His job is just to give a fair decision. In such a case, why was Ubhaya Bharati allowed to ask a question?
2) Adi Shankaracharya was an expert in Advaita, religion and philosophy. Why was it necessary for Shankaracharya to answer a question related to Kama? Example: An expert in physics need not answer a question related to surgery. Moreover in a seminar of physics, people will not entertain question unrelated to that topic. Hence Shankaracharya could have simply bypassed the question as it was not related to the topic of discussion.