is this the most common word for return? i've heard γυριζω and ξαναρχω but never this
Yes, it is. Γυρίζω is also used but has other meanings, too, and ξανάρχομαι means "come again".
Is "She is returning" a correct translation? If not, why not? It was marked wrong — written Greek to English, free-form text, mobile (Android).