(1). yes.
(2). no.
Does "(12031283)the head lama of the Karma Kagyu lineage of Tibetan Buddhismrejected Kublai's invitation, so instead Kublai invited Drogon Chogyal Phagpa (12351280), successor and nephew of Sakya Pandita, who came to his court in 1253." correctly answer the question of With whom did Kublai Khan have a unique relationship with?
(2).