Is the sister who claims that a transparent paper has descended from the sky containing the Beautiful Names of Allah, and that Al-Khidr came to her to inform her of the unseen, and that she has become one of Allah's righteous saints, while continuing to display herself immodestly—is she mentally ill or possessed by a jinn?

What has been mentioned about this woman is closer to madness. The characteristics of the righteous saints of God are based on uprightness and adherence [to divine law]. God may bring about extraordinary events through some individuals, but only the ignorant are deluded by them. As for Al-Khidr, the preponderant opinion is that he is no longer alive, and even if we assume he is, he does not know the unseen, which God alone possesses.