"Nobody brought the phantom punch, did they?"

"Nobody" is a negative word, so the tag must be positive. Even though "nobody" takes a singular verb in a sentence, its question tag uses the pronoun "they."

"Everyone is having a terrifyingly good time, aren't they?"

"Everyone" also uses the pronoun "they" in question tags. Because "they" is plural, the verb changes from "is" to "are," creating the negative tag "aren't they."

"Nothing ever goes wrong at these parties, does it?"

"Nothing" is a negative word and refers to an object/concept, so it takes the pronoun "it." Since the statement is negative, the tag must be positive ("does it").