Is it permissible to give zakat to the daughter of a deceased brother, who has apostatized from Islam and converted to Christianity, and who is asking for money to help with her living expenses, under the category of "those whose hearts are to be reconciled (to Islam)"?

Zakat is not given to an apostate from Islam because he is a disbeliever. Zakat is given to those whose hearts are to be reconciled (Al-Mu'allafatu Qulubuhum) so that they may enter Islam or be firm in it. These refer to influential leaders, not individuals. The apostate niece can be treated with kindness and beneficence, and efforts can be made to invite her, visit her, and persuade her to enter Islam. She might return to Islam by leaving her current environment and entering the environment of Muslims.