因为句子是一般过去时 要求一般疑问句 所以用did 提问
Did you want me to buy a gift for your father?
对 I 提问 是 Who wanted me to buy a gift for your father
对 a gift 提问 是 What did you want me to buy for my father?
对 my father 提问 是 Who did you want me to buy a gift for?