Will one who slept through the time of a prayer, and who was suffering from a touch [of jinn] and could not wake up for the prayer despite his attempts, be counted among those who are punished for missing prayers?

If sleep overwhelms you and the prayer time passes without intention, then there is no sin upon you. For the sleeping person, the pen is lifted, and "there is no negligence in sleep; rather, negligence is upon him who does not pray a prayer until the time for the next prayer arrives." One should strive to fortify oneself with supplications and remembrances, and take measures to wake up for prayer.