"In which country do you live?"
Translation:В какой стране ты живёшь?
I do not know if that word order is wrong, but I have more often seen the "question" part first (unless it is a yes / no question, which reads as a normal sentence).
Here, the "question" word is какой, so "в какой" would go first with typical word order. Just like что, кто, чьё etc go first when asking a question.
"какой" is the prepositional of "какая". Prepositional is used because of "в" to indicate "in".
The prepositional of "какой" would be "каком".
You can check the full table here:
Yes, just like English "in". Otherwise it would be "Which country do you live?", which is generally wrong or at least a very unusual question (what does it mean "to live a country"? ).
Note however that "страна" is feminine. "Какой" is the prepositional of (nominative) "Какая", and not the nominative masculine "Какой", because of "В". The hypothetical strange question without "в" would read
Какая страна ты живёшь?