Is the discourse mentioned regarding the benefits of menstruation and the reward and forgiveness resulting from it, and what was attributed to the Prophet, may Allah bless him and grant him peace, and Aisha, may Allah be pleased with her, authentic?

The first report is false, has no basis, and it is not permissible to narrate it. The second tradition is no better; signs of fabrication and falsehood are clear upon it. If any of that were true, there would have been ample reasons to transmit it, and the authors would have mentioned it.