This cannot be "Where was your sister living"?
It 100% can be.
This section is frustrating. Always refusing "was /were ... ing"
Твоя is pronounced as Твоей.
I heard that on mine as well.
But in slow mode (the turtle) it sounds right, like твоя.
Shouldn't it say "где жила твою сестру?"
No. "To live" is intransitive - "I live", "She lives", etc. Сестра is in the nominative, she is the subject, and жить is conjugated to match that (singular, feminine actor in the third person).
spelling mistake in the expected answer
How would I say "Where had your sister lived" in Russian ?
It would be the same - Russian has just the three tense aspects (past, present and future), and the meaning of something like "Where had she lived?" would require additional context.
тогда : у тебя очень интересная сестра ---
сейчас : где жила твоя сестра? ---
а будит? :)