Is it permissible to publish da'wah messages quoted from the sayings of scholars and the website, and is that considered an infringement of their rights? And is it considered correct to transmit answers from the website to others?

The fundamental principle regarding the uncredited نقل (transmission) and اقتباس (quotation) from scholars is that there is no harm in it. Indeed, scholars have transmitted from one another without attribution. However, it is preferable to attribute the statement to its speaker, as this is part of the blessing of knowledge. Nevertheless, it is not permissible to create the illusion that the transmitted material is the original creation of the transmitter, as this constitutes cheating and being "filled with what one has not been given." As for the contemporary academic convention which requires attribution and considers its absence a breach of scholarly integrity, it does not render the transmitter sinful, as long as he does not create the impression that he originated the transmitted material.