__your brother and you __(have) any questions？

Does your brother and you have any questions?

好像是个什么就近原则的。

我觉得类似于我们中文的“大喘气”，说话者可能开始只想问if your brother have any questions, 后来临时and you。

Do ... have
have and question是内心思想活动 所以用一般现在时 do （之前有位说用did 如果不是在单一句子而是在某些特定语境或有其他时间状语从句时当然可以用did）
因为是your brother and you就是2个人 当然不能用does

do, have
或者did, have

两种语境，但是绝对都正确

Between ... have

did have