All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible for an orphan boy to marry your daughter and it is permissible for your son to marry an orphan girl.
An orphan girl is given in marriage by her guardian. If she has no Muslim guardian, then it is a Muslim judge or someone who serves in place of one who gives her in marriage. If there is no Muslim judge and no one to serve in place of one, then she should appoint a trustworthy Muslim man who authorizes her marriage.
It should be noted that it is not permissible for a non-Muslim man to marry a Muslim woman, and it is not permissible for a Muslim man to marry a non-Muslim woman unless she belongs to the People of the Book and she is chaste.
Secondly, it is permissible to pay Zakah to orphans if they are needy. Therefore, if these children fit this description, then it is permissible to get support for their care, and this must be spent according to their needs. Please refer to Fatwa 83451.
Finally, please note that the Islamic guidelines should be observed if the orphan girl is a non-Mahram to her sponsor if she reaches puberty; the same applies to the orphan boy when he reaches puberty with respect to female members of the sponsor's family of the sponsor, like his wife and daughters. Please refer to Fatwa 88924.
Allaah Knows best.