My father owns a school where there is free mixing. Is his income halal ? Will our du'aas be accepted since the food and clothing of the person making du'aa should be from halal income ?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

If the purpose of owning the school was for permissible education, then the fee that your father takes from students or others is permissible. However, if the purpose is to teach forbidden things, such as teaching deviant beliefs and concepts, then the fee that your father takes from students or others is impermissible. As for the forbidden mixing, if it is being practiced, then the one who is in charge of the school bears the sin by allowing it in his school, but the payment the owner receives from leasing his school for permissible education is not forbidden to him.

To sum it up, fees taken for a forbidden purpose are impermissible and it is one of the obstacles that prevent supplications from being accepted, and fees taken for a permissible purpose are permissible.

Allah knows best.