Is the daughter of a husband from a previous wife—whose mother is still alive—considered an orphan, and is taking care of her rewarded with the reward of caring for an orphan? And how should I deal with her and with this situation?

First: An orphan is a young child whose father died before he reached puberty. Sponsoring this girl carries a great reward, and it may be greater than sponsoring an orphan. It is part of preserving a believer's "loss" for his fellow believer, as stated in the noble Hadith: "A believer is a mirror to a believer, and a believer is a brother to a believer; he wards off loss from him and protects him from behind."

Second: Obeying the husband and being kind to his daughter is part of his rights upon the wife, as stated in the Hadith: "If a woman prays her five [daily prayers], fasts her month [Ramadan], guards her chastity, and obeys her husband; she will be told: Enter Paradise from whichever of its gates you wish."

Third: The wife must not allow the child to affect her relationship with her husband, and she should help him in raising her and being kind to her. The wife will see the fruits of this in this world and the hereafter, and her husband's love for her.