συζούν = ζουν μαζί
Of course!!! Added :D
Could επειδή be used instead of γιατί?
Absolutely, and it may be more correct (why=γιατί, because=επειδή)
γιατί is not only "why" but also "because".
γιατί is like για τι=for what, which kind of links the meanings nicely (at least in my head lol)
μενουν μαζι was rejected
That's one of the accepted translations. What was your full answer?