Learn Spanish (Spain): ¿Vuestra madre vive con vuestra abuela? - Does your plural mother live with your plural grandmother?

Possessive words in Spanish have to match the gender and number of the thing being owned, not the person who owns it. Because madre and abuela are both feminine and singular (just one mother, just one grandmother), we use the feminine singular form vuestra.

What is the difference between vuestra and tu since they both mean "your"?

We use tu when speaking to just one person. We use the vuestro family of words when speaking informally to a group of people in Spain. It is the equivalent of saying "you guys's" or "y'all's" in English.

If we are talking to a group of people ("you all"), why is the verb vive in the "she" form rather than the "you all" form (vivís)?

The verb always matches the person or thing doing the action. Here, the subject doing the living is "your mother" (vuestra madre). Since she is one person (she/ella), we use the third-person singular form vive.

Why doesn't this sentence use a word like "Does" to start the question?

Spanish doesn't use helper words like "do" or "does" to make questions. You can just use the normal statement word order and add spoken question intonation, along with the upside-down and regular question marks in writing.