What is the ruling on transmitting ideas or sentences from an illegally photocopied book for use in writing or authorship? Is it permissible to publish images from it while citing the source? And what is the legitimate way to benefit from its content?

Downloading illustrated books follows the ruling of printed books: if permission is granted to copy them, then there is no harm; otherwise, it is not permissible. As for quoting ideas and citing what is in it, it is permissible with attribution to its author, and this is a legitimate benefit that is not prevented by the author having registered otherwise. As for the benefits gained from reading books copied without right, there is no harm in benefiting from them.