Is it permissible to read Islamic books if the source of the money used to purchase them is unlawful or dubious, and what should be done with the books if they are unlawful, and is it permissible to use them?

There is no harm in benefiting from something bought with unlawfully acquired money, because the unlawfulness of the money pertains to the liability of its possessor, not to the money itself. What is obligatory is to repent from taking unlawfully acquired money and to dispose of it. As for money about which there is doubt, its unlawfulness is not determined merely by doubt, and the principle is that certainty is not removed by doubt, even though disposing of it is more preferable.