Is it true that the prayers of one whose lawful and unlawful money are mixed, or one who commits grave sins, or one whose money and food are unlawful, are not answered?

Consuming unlawful (haram) earnings is a reason for prayers not being answered. However, Allah Almighty may answer the supplication of an individual due to another reason, such as being in dire necessity (al-idtirar), or if the person persists in consuming unlawful earnings.

There are many impediments to the answering of prayers, including consuming unlawful earnings and persisting in major sins. But this does not mean that prayers are never answered for someone whose money is unlawful, for Allah answers the supplication of those in dire necessity.