Can jinn touch people, and if so, how will the possessed be held accountable for their actions on the Day of Resurrection?

Yes, jinn can afflict humans with "mass" (demonic possession), and this is established by the Qur'an, the Sunnah, and the consensus of the Ahl al-Sunnah wal-Jama'ah (Sunni Muslims). This is alluded to in the verse: "Those who consume interest will not stand [on the Day of Resurrection] except as one stands who is being beaten by Satan into insanity." (2:275) "Mass" is a type of illness. If the afflicted person is sane and acting out of free will, then they are held accountable for their words and actions. However, if the "mass" overcomes them and deprives them of their sanity and free will, then they are like a mad person and are not subject to religious obligations. The term "mass" may also be linguistically applied to "insanity." Nevertheless, if the afflicted person, while in a state of insanity, assaults someone and destroys their property, they are liable for that property. The jurists have unanimously agreed that the insane person is not held accountable for religious obligations, and their verbal actions are invalid. However, the rights of other people do not fall away from them; thus, they bear financial responsibility for the damages they cause.