The correct answers are Everybody loved my spicy soup, didn't they?, Nobody remembered to buy the truffles, did they?, and Someone left the oven on, didn't they?.

When the subject of a sentence is an indefinite pronoun referring to people (like everybody, somebody, nobody, anyone), we use the pronoun they in the question tag.

Also, remember that nobody makes the sentence negative, so it requires a positive tag (did they? instead of didn't they?).