Usually in writing the other person goes first, but if you were to say it out loud both are fine.
Correct.
Both sentences are grammatical and can be used interchangeably. They differ only in the word order of "your sister" and "you." In English, the subject and verb in a sentence can usually be rearranged without changing the meaning or grammatical correctness. So both sentences are correct, but the second one ("What time do you and your sister get up?") is more commonly used in everyday conversation.
