Is a doctor obligated to refuse to treat someone whose money he knows to be unlawful, or should he treat him and accept the money? And how does one generally avoid doubtful matters?

If the owner of ill-gotten gains has all his wealth from unlawful earnings, then it is absolutely impermissible to transact with him using his wealth. However, if some of his wealth is lawful, then transacting with him is not forbidden. The principle is that what is in people's hands belongs to them, and there is no need to inquire about the source of wealth of someone one transacts with, unless it is known that the money is stolen or usurped, in which case it is not permissible to take it. But if the status of the money is unknown, or if its owner is known to have unlawful elements in his wealth, then the unknown is like the non-existent. And whoever refrains from transacting with him out of piety, if his wealth is mixed, has committed an innovation.