Do the alms (sadaqah) given by brothers to their incapacitated, unemployed brother count as acceptable charity? And is it permissible for him to receive zakat from them?

Whether charity is accepted or not is part of the Unseen. Scholars judge an action based on its validity. It is permissible to give voluntary charity to relatives; in fact, it is recommended to give charity to them, and the reward for it is multiplied (charity and maintaining kinship ties), as the Messenger of Allah (peace be upon him) said: "Charity given to the poor is a single charity, but charity given to a relative is two: charity and maintaining kinship ties." As for obligatory charity (like Zakat), it is permissible to give it to a brother if he is among the categories eligible for Zakat (the poor and the needy).