Is it true that the misdeeds of those who have been backbitten are cast upon the backbiter, under the names of these misdeeds (such as adultery and drinking alcohol), if his good deeds run out, and is there a clear hadith that indicates this?

No Hadith states that the sins of disobedient people are recorded in the scroll of those whom they backbit. Such a claim cannot be made without a legal text.

However, it has been narrated that the sins of the oppressed will be cast upon their oppressor on the Day of Judgment if the oppressor's good deeds are exhausted. This is as stated in the Hadith of the pauper, who insulted, slandered, consumed wealth unlawfully, shed blood, and struck others. The oppressed will be given from his good deeds, and if his good deeds are exhausted before he repays what he owes, then their sins will be taken and cast upon him, and then he will be cast into the Fire.