"Is her mother alive?"
Çeviri:Onun annesi hayatta mı?
We cannot use ''onun annesi canlı mı?'' because in turkish,unlike english, canlı/alive is generally used when we talk about life/death situation of an animal. Kedi canlı mı?(Is the cat alive) As an exception,if we talk about all beings as a whole,we can use the word ''canlı''. İnsan en vahşi canlıdır.(Man is the crulest animal) so to speak,if we consider humans as an animal in a scientific or philosophic context we can use the word ''canlı''.
Bear in mind that ''can'' means life in turkish,can-lı means the one who has a life.
Hope this helps.Best regards!