Ubhaya Bharati's questions are given in this excerpt from the Madhaviya Shankara Digvijaya, the traditional biography of Adi Shankaracharya:
Discuss with me the science and the art of love between the sexes (Kusumastra sastram). Enumerate its forms and expressions. What is its nature and what are its centres? How does it vary in the sexes during the bright and dark fortnights? What are its manifestations in man and woman?
Note that Adi Shankaracharya never actually answered these questions. This later excerpt from the Madhaviya Shankara Digvijaya says that when Adi Shankaracharya comes back for the debate, Ubhaya Bharati, who is considered by Advaitins to be an incarnation of Saraswati, leaves this world and goes to Brahmaloka.
But if for some reason you still want Adi Shankaracharya's insights on this subject, this excerpt from the Madhaviya Shankara Digvijaya relates that while Adi Shankaracharya inhabits the body of the king Amaruka, he composes a work on Kama:
Besides, he studies during this time the Sutras that the sage Vatsayana had made on this subject together with all the commentaries on the same, and had also produced a new work of great profundity on the theme, bearing the name of Amaruka.
That work is the Amaru Shatakam, and you can read it here. Some Advaitins claim that in this work Adi Shankaracharya merely used the language of Kama to convey the ideas of Advaita. Personally, I'm not a follower of Adi Shankaracharya so I'm skeptical of this story.