A bit late, but I'll comment this just in case anyone else has this question. The reason the word "vivir" is conjugated (to change a verb's form to fit different persons, tenses, etc.) as "vive" and not "vives" is because tu is just a possessive adjective modifying hijo, not the subject (which would be tú, with an accent). Hijo is the actual subject. Imagine if the sentence were "¿Dónde vive el hijo?" ("Where does the son live?"). In that case, it's easier to see that "hijo" is the actual subject. In both cases, the son is the one doing the action being asked about, not "you."
Generally in questions that start with question words (interrogatives), the word order is interrogative + helping (auxiliary) verb + subject + main verb. El sujeto está entre el verbo auxiliar y el verbo principal:
Where do you study? ¿Dónde estudias?
When does he arrive? ¿Cuándo llega él?
What is she doing? ¿Qué hace ella?
Why do they say that? ¿Por qué dicen eso?
Where does your father work? ¿Dónde trabaja tu padre?
How are your sister's children feeling? ¿Cómo se sienten los hijos de tu hermana?